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There are several outputs of a numeric computations, I'm seeking a method to model them with a general statistical model (e.g., distribution function).
For example:
...
0.044423
0.127713
0.010692
0.019980
0.013242
0.071450
0.054766
0.013618
0.067680
...
Each series has different length. Intuitively, Statistica has an... |
I have a question on the distribution of betas in a multiple linear regression scheme
The estimated parameter vector is $\hat{\beta}=(X^′X)^{−1}X^′y$ where $X = [1 \; \;x]$ is the $n \times 2$ data matrix.
Substitute $X \beta + \epsilon$ for y.
Calculate $\text{var}(\hat{\beta})=\text{var}[(\beta+(X^′X)^{−1}X^′\epsilon... |
Here I described my general situation. How to calculate 95%CI between means in R?
|
Let's suppose I have a set of measurements on a continuous variable which follows a power law distribution, and I’m interested in deriving the exponent of such a distribution.
So far I've used the binning method, so I was dividing the interval in n bins, plotting the number of observation for each bin in log-log scale... |
What is the practical way to identify the factors that create variation in a data of a dataset? What category does this question fall into? Are there a set of algorithms that can be used for this purpose? Statistical modeling solutions? I googled a lot but no go! The question is so vague that hard to find an answer for... |
I have data with continuous class and I'm searching for good methods to reduce number of attributes. Now I'm using correlation based filters, random forests and Gram–Schmidt algorithm.
What I want to achieve is answer which attributes are more important/relevant to class attribute than others.
By using methods that ... |
I am working on a text classification problem. My data is highly imbalanced. For example, one category has 700 documents while the other has 30. I have around 30 categories. I tried different classifiers and the performance is consistently poor.
What is the best way to tackle this issue? Thanks
|
I'm trying to reduce dataset dimensionality. PCA is a good metric but that gives me new dataset. My goal is to determine from number of events (e.g. 60) and number of trials (e.g. 6) which events are more relevant.
For example:
1st, 3rd, 21st, 45th ... (N total) events are good enough to approximate behavior of data... |
I am working on a machine control project. We can measure the motor's current during operation. Sample data from two motors performing an operation successfully is below. The red trace shows the current from one motor, the blue trace the current from another. I'd like to try and come up with an algorithm for identi... |
Are there any multi-variate continuous distributions whose probability distribution functions give high values for sparse vectors and low values for dense vectors, i. e. indicating the sparseness of the vector?
I found one sparseness measure in [1] which is as follows for $x \in \mathbb{R}^n$:
$$s(x) = \frac{\sqrt{n}-\... |
I'm trying to label a pretty simple scatterplot in R. This is what I use:
plot(SI, TI)
text(SI, TI, Name, pos=4, cex=0.7)
The result is mediocre, as you can see (click to enlarge):
I tried to compensate for this using the textxy function, but it's not better. Making the image itself larger doesn't work for the dense ... |
Suppose we have some data (say around 10,000 cases) that sample a variable of interest; e.g., the concentration of metal in soil. By generating a random series of indices we choose some of those samples and then compute some statistics, for instance the mean. We do this many times and finally get the mean of mean valu... |
Consider the random variable $y_M$ which equals the sum of $M$ independently uniformly distributed random variables; i.e., $y_M = x_1 + x_2 +\ldots + x_M$, with the assumption that each of the $x_i$ are independently and uniformly distributed. The variance of the sum equals the sum of the variances of each of the $x_i$... |
If I am trying to generate hypotheses, what are the drawbacks of setting my p-value cutoff after looking at the various p-values I get for my set of results?
For instance, if I initially did a large number of experiments looking at the effects of several thousand chemicals individually on cell growth and I find that th... |
I did a simple physics experiment that measures the attractive force a plate experiences towards the other plate as a function of the applied voltage and distance between the plates. Now I have to know whether the gathered data confirms the relation $F \propto V^2/d^2$. Suppose the following is what I gathered.
voltag... |
Is there a method for (nonlinear? kernelized?) regression of functions with output in projective space? That is, given a series of examples $x_i\in\mathbb{R}^n$ (or $x_i\in\mathbb{P}^n$) and $y_i\in\mathbb{P}^m$ (so, $\forall c\in\mathbb{R}, y_i=c\cdot y_i$) such that $f(x_i)=y_i$, can I write down some function that... |
I have two devices, and I'm trying to figure out which one of them is preferred by users.
Thirty people have rated each device on a 12-item questionnaire which asks them to grade the device on 12 parameters.
What statistical tool should I use to decide which device is better? (just comparing the grades is not enough)
... |
I am currently using the simple slope analysis to examine the significant interaction effects between my continuous moderator and a dichotomous predictor (values 1 & 2)on a continuous DV. I have 2 continuous covariates in the analysis.
My simple slope graph however showed negative values in the DV (i.e: moderator valu... |
I am estimating a structural equation model in which two latent variables (with 4 indicators each) and the interaction between the two latent variables predict a single observed variable. I would like to save the individual residuals from the observed endogenous variable to use in further analyses. As far as I can tell... |
Does anyone know how to use (nlme)? I'm having a lot of problems using it for something that should be really simple, any help would be really appreciated. I won't put up the details until I know someone knows what I'm talking about.
Data was collected by a field study concerned planting pattern, genotype, we replicate... |
I wish to simulate from a normal density (say mean=1, sd=1) but only want positive values.
One way is to simulate from a normal and take the absolute value. I think of this as a folded normal.
I see in R there are functions for truncated random variable generation. If I simulate from a truncated normal (truncation at... |
I'm using a 1.6M tweet corpus to train a naive bayes sentiment engine.
I am trying to "compute the entropy of a probability distribution of the appearance of an n-gram in different datasets". My two data sets are n-grams constructed from a positive corpus & negative corpus, and I want to remove any common n-grams with ... |
I have seen many reports which include (say) 6 scatter plots in one big table like format. Each scatter plot shows the relationship between two different variables. For example, one may show the relationship between income and expenditure and another may show the relationship between mortgage payment and holiday taken.... |
I have a three point Likert scale question:
How happy are you?
1= low levels of happiness
2= medium levels
3= high levels
I want to do multiple linear regression on the variable. I am making the assumption that that it has the same difference between low and medium and medium and high. I want to treat... |
I am dealing with an existing algorithm where data is processed as follows:
We have a large sample of data taken every minute, this is grouped into 'buckets' of data for every hour.
(Each bucket contains a SUM(), MAX(), MIN() and the number of data points taken in the hour.)
Now, ideally there should have been 60 sampl... |
I'm sorry if my terminology is wrong, I'm making it up.
I have hundreds of objects counted simultaneously in two treatments, each measured three times (not in pairs). e.g.:
A1 A2 A3 B1 B2 B3
Object 1 2 4 3 5 8 1
Object 2 0 0 0 0 0 0
Object 3 20 15 12 1 0 3
Object 4... |
There are a lot of outstanding machine learning/data mining standalone applications available in different languages like Java, Python, and others.
However, I wonder, practically, in case of applying machine learning techniques into a web environment, is there anything existing that can be handy to use? E.g. any framew... |
In geostatistical context it is common practice that for simulations of a variable of interest (e.g., grade of concentrations of metal in rock samples) the number of simulations at least needs to be 30. I would ask what the criteria is to choose a right trial number considering that each trial has an expense of large c... |
Is there any simple (or simplified) explanation for how stochastic simulation work? How those methods could provide the information about the underlying processes that almost impossible to be achieved with non-stochastic models? How stochastic (random) model could link with unknown property of the system?
For example, ... |
I recently wrote a program that graphed data points so that a user could scroll through them and find "interesting" parts of the data.
Now I am looking at ways to make it even simpler by making a table of values deemed to be interesting. These are usually either the value switching to a new value, or spiking and return... |
For my thesis I will need to do an experimental user study to compare two user interfaces which both can perform the same tasks. They differ in how they support you in achieving your task. I'm not that familiar with statistics so please correct me if any of the following assumptions I already made are incorrect.
I'm pr... |
I want to detect seasonality in data that I receive. There are some methods that I have found like the seasonal subseries plot and the autocorrelation plot but the thing is I don't understand how to read the graph, could anyone help? The other thing is, are there other methods to detect seasonality with or without the... |
Background
I have developed a recent interest in Item Response Theory and its applications. I am studying clinical psychology and am most interested in polytomous models aimed at modelling psychopathology (e.g., a depression measure that uses likert scales). Specifically, I am interested in how certain measures can dis... |
I'm trying to model some chemical data from a series of spectra. I've gone through the preprocessing step and selected "autoscale" (I'm using Pirouette). And when it comes to validation I'm a little confused as to which one (step or cross) will yield a model that has a good predictive capability. Any insight would b... |
I have 1 dimensional data series sampled at even time intervals; they are noisy but have the exactly the same (unknown) underlying curve - with one difference: they are offset in time by some unknown tau. What is the best (most robust) estimate of that tau? Also, what is an estimate that can be calculated quickly (that... |
Let's say you're running an A/B test on a website. Let's also say the standard methodology of randomly displaying one version or the other is unusable due to SEO hand-waving. The particular page under test is localized to each city, so the best testing methodology your one stats-educated programmer could come up with... |
I would like to understand how can I check if some points around a line have constant distance between the point and the line.
So image a normal chart(cartesian plane) with a line that is formed with points where its coordinates are: x > 0 and y > 0 so always numbers bigger then zero.
Then, when I have this line i need... |
I am searching for existing datasets that we can use to test several datavis techniques we are researching.
I know several resources like those included in R (try plot(Orange) or see here).
But I'd like to take it one step forward:
Which are the best real-world datasets to test a visualization tool?
Which datasets hav... |
Are there any tools in R that could be used to optimize the allocation of customers amongst possible offers, given constraints? Can anyone give hints/examples on their use? Hope my setup makes sense...
Here is the problem setup:
There are the following:
$N$ customers ($N$ is large)
$F$ offers (the offers that can be m... |
I got a bit confused about how to fit a local polynomial to binary outcomes if I would rather approximate the underlying index (within a link function) instead. (Basically for the same reason why someone would estimate a logit or a probit instead of a linear probability model.) Of course, I would like to plug the varia... |
I conducted a survey asking people of various income groups about their annual expenditure under various consumption brackets such as food, clothing, housing etc. I then calculated the amount spent by people of different income brackets in these categories as a percentage of their total income. Now, to plot this data a... |
I constructed a model via multinominal logistic regression analysis. The final model contains three predictors. All predictors are significant when they are the only predictors. However, the coefficient of one of the predictors is not significant when included all three predictors are included in the model.
Should I in... |
I have a list of numbers that, when plotted on a graph, clearly demonstrate trends such as rising upwards, dropping, repeating etc.. When a human sees the graph, they can easily make out what's happening. What I'm trying to do is achieve the same thing numerically and have the system detect what trends are occurring in... |
Imagine I have measured heights of humans (in cm) and show the data in a histogram:
# Generate sample data
sampleSize = 100000
sampleData = round(rnorm(n = sampleSize, mean = 175, sd = 14))
# Draw histogram of sample
h = hist(sampleData, breaks = max(sampleData) - min(sampleData), plot=T)
Now I want to know how reali... |
I have two questions about confidence intervals:
Apparently a narrow confidence interval implies that there is a smaller chance of obtaining an observation within that interval, therefore, our accuracy is higher.
Also a 95% confidence interval is narrower than a 99% confidence interval which is wider.
The 99% confidenc... |
I have a doubt regarding the variance, I try to explain It with an example.
I have two vectors, like:
a <- c(1:10)
1 2 3 4 5 6 7 8 9 10
b <- c(10:1)
10 9 8 7 6 5 4 3 2 1
the variance is obviouly the same:
> var(a)
9.166667
> var(b)
9.166667
Ok, I need to test if the variances are similar, and for th... |
I've been trying to code an algorithm to suggest bets in 1X2 (weighted) games.
Basically, each game has a set of matches (home vs away teams):
1: home wins
X: draw
2: away wins
For each match and symbol (1, X and 2), I will assign a percentage that represents the chances / likelihood of that symbol being the correct... |
I have a simple model without interaction and it stated significant effect for all the explanatory variables (continuous variable rok and categorical variables obdobi (levels hn and nehn) and kraj:
Call:
glm(formula = cbind(ml, ad) ~ rok + obdobi + kraj, family = "quasibinomial")
Deviance Residuals:
Min 1Q ... |
In R I would like to solve a system of linear equations with constraints to preserve monotonicity. I can do this easily with no constraints on the coefficients. Here is an example:
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.6945405 0.1157702 0.004973632 0.0000000 0.00000000 0.00... |
I'm creating a large contigency table to summarise the difference between a bunch of (categorical) demographics across groups. I would like to know what the confidence intervals are for each cell in the proportional cross-tab, and if the proportion of each demographic group in each sample is statistical different from... |
The actor-critic model is used within temporal difference learning, which is a method within reinforcement learning, to optimize a process on a state-by-state basis by using the difference between performance and expected performance for each respective state. In other words, there is a set of possible input patterns t... |
What do you call an average that does not include outliers?
For example if you have a set:
{90,89,92,91,5} avg = 73.4
but excluding the outlier (5) we have
{90,89,92,91(,5)} avg = 90.5
How do you describe this average in statistics?
|
We have a daemon that reads in data from some sensors, and among the things it calculates (besides simply just reporting the state) is the average time it takes for the sensors to change from one value to another. It keeps a running average of 64 datapoints, and assumes that runtime is fairly constant.
My obvious solut... |
I am trying to visualize a large multi-dimensional dataset. Each dimension has a different range. Values in one column may range between 0-100 while values in another could range from a few hundred thousand to a few hundred million. Therefore it is really hard to show a graph with a reasonable scale. I would like to vi... |
I need to check if two price lists move togheter. I three methods:
Pearson
Spearman
Kendall
Could someone explain me why I should use a method instead of other to check if those price lists move in the same direction? I know that Pearson is often used for this kind of analysis... Is that correct?
Thank you
|
Is there a difference between the phrases "testing of hypothesis" and "test of significance" or are they the same?
After a detailed answer from @Micheal Lew, I have one confusion that nowadays hypothesis (e.g., t-test to test mean) are example of either "significance testing" or "hypothesis testing"?
Or it is a combina... |
For some Y variable, that is divided into 3 groups (X), I wish to compare the groups and for the hypothesis that the 90% quantile is the same between all three groups. What tests can I use?
One option I can think of is using quantile regression, are there other alternatives/approuches?
I imagine that if I had wanted t... |
Background:
In mining engineering, sampling is used to get the rate of concentration of minerals in rocks. Sampling procedure is carried out in the field on the area being explored at the predefined coordinates (x,y) according to designed maps. So there are lots of samples from surface materials i.e., rocks/soils/water... |
Context:
I am running a large survey and am trying to figure out what statistical analyses to perform.
The survey asks questions in every format known to man (e.g., likert scales, multi-choice, dichotomous) and is about psychosocial health and work stress.
I plan to run a factor analysis to see what demographic questi... |
I do not have any idea how to calculate this, but I do have the data points available.
I have a computer system that has a setting for something -- garbage collection ("gc") -- to occur with p probability on any given time that a certain process runs (I'll call that process "the process").
I have the frequency of the p... |
I have data that I believe is sinusoidal, but I don't have an integral
number of periods. How do I find the "best fit" Sin/Cos function,
compensating for this and for the ugly constant that appears? EXAMPLE:
Here is some data that follows a sinusoidal pattern (Mathematica format)
t4 = N[Table[Sin[3.17*2*Pi*x/200],... |
In some sense the multivariate normal is the "nicest" distribution that we can describe using only a vector (rank one tensor) and a symmetric positive definite matrix (rank two tensor).
$$\mathcal{N}(\mu_i, \Sigma_{ij}) = |2\pi\Sigma|^{-\frac{1}{2}}e^{-(x-\mu)^T\Sigma^{-1}(x-\mu)}$$
Is there a generalization to highe... |
I have 20 correlation coefficients (r) to report, for example, .34, .45, .67, .23. and so on. These are correlations between Variable A and Variable B, based on gender, age, education levels etc.
I am after a succient method to show all the correlations in one glance. Is there any best practice in regard to reporting ... |
I have an intuition that re-casting the Poisson binomial distribution probability mass function in the following way might lead to a more elegant closed form than the DFT approach:
Sum the $\log_2$'s of the probabilities of each independent trial. The negation of that sum is equivalent to a new number of trials each of... |
Instead of this simplified-version of this file:
#!/usr/bin/env python
import numpy as np
import pylab as P
data = [x.rstrip().split("\t") for x in file(".data", "r").readlines()]
sdData = [float(x[1]) for x in data]
retData =[float(x[0]) for x in data]
# Calculating medians for estimating mean and sd
sdMed = sorted... |
I'm using the Fligner-Killen test to analyze the residuals of a linear regression.
I subdivide those residuals in three groups and then I do the FK test to check the homogeneity of variances.
The result is:
fligner.test(pair.res, pair.groups)
Fligner-Killeen test of homogeneity of variances
data: pair.res and pa... |
Hopefully someone on these forums can help me out with this basic problem in gene expression studies.
I did deep sequencing of an experimental and a control tissue. I then obtained fold enrichment values of genes in the experimental sample over control. The reference genome has ~15,000 genes. 3,000 out of 15,000 genes ... |
In OLS, is it possible for the $R^2$ of a regression on two variables be higher than the sum of $R^2$ for two regressions on the individual variables.
$R^2(Y \sim A + B) > R^2(Y \sim A) + R^2(Y \sim B) $
Edit: Ugh, this is trivial; that's what I get for trying to problems issues that I thought of while at the gym. S... |
I am testing the fit of my mediation model in AMOS, and the model fit statistics are very strange. For example, the CFI is .000 and the RMSEA is way too big (14.774). It seems as though there has been some error with the data or the calculation, but there is no indication of what this might be. What do these strange re... |
Context:
I have a study where six numeric variables are measured in each of two repeated measures experimental conditions (n = 200). Lets call the conditions $A$ and $B$ and the variables $A_1, A_2,..., A_6$ and $B_1, B_2,..., B_6$. Theoretically, I expect that in condition $B$ more variance in the variables should be ... |
Can someone give an explanation for why the t-test "happens"? I was taught to use the t-test when you don't know the population standard deviation (i.e., you only know the standard deviation of your sample), but I'm not sure why that would make it different from a z-test.
|
Background Context:
I am amazed at the complex statistical questions people ask on this site and I have learnt a lot from them. Thank you all!
However, I have focused on correlation because it is the easist method to understand for a person like me who has no formal training in statistics but is required to do market r... |
I've encountered this sentence while reading an article on sciencemag.org.
In the end, responses from just 7600 researchers in 12 countries were included because the remaining data were not considered statistically significant.
Is this a proper way to do research? To leave out results because they were not consider... |
I have data that involves 2 groups (equal sample size in each) and data for each group over 3 time points (they are actually 3 different monetary reward conditions). I want to investigate within group differences. All time/condition points are important, I don't have a "control" time point.
Any opinions on the followin... |
I have a 5 x 2 design where one of the levels of the first factor is a control, all others are experimental conditions. I'm interested in the interaction between the two factors and especially, if the interaction is present for each of the 4 experimental conditions with the control condition.
I conduct 4 separate 2 x 2... |
Following cardiac surgery, patients are encouraged to exercise regularly (assume that regular exercise is defined as exercising on 3 or more days per week). A physician suspects that patients exercise regularly immediately following cardiac surgery but tend to reduce, even stop exercising completely, over time. An inve... |
Context:
Poisson point processes (PPP) are widely discussed in the literature.
In the following figure a framework to generate two-dimensional PPP is demonstrated. First the area being studied (part of space which can be in 1D, 2D, 3D, ..., in our example is a 2D shape i.e., square) is divided into cells (gridding). Se... |
I have a set of 3D points. The points have three components $x$, $y$, $z$. You can think of these points as the surveyor points that one collects from measuring a terrain for GIS purposes.
I have a few algorithms that take in this set of 3D points as the reference and also a list of 2D points $p_{out}(x,y)$: the algori... |
My website has advertising for various companies - say 10,000 companies. Each company has it's own page but all the pages are currently similar except by which company is on the page. A success/response/dependent variable is a visitor clicking on the advertisement. Each company's page has a different success rate - ... |
My dependent variable are reaction times (RTs) in a psychological experiment. The experiment features a control condition and an experimental condition and for each subject, I have several hundred realizations of each condition (the variance in this experiment is pretty large, both the intra- and inter-individual). I c... |
I'm a high school student and I'm working on a computer programming project, but I don't have a lot of experience in statistics and modeling data beyond a high school statistics course so I'm kinda confused.
Basically, I have a reasonably large list (assume it's large enough to meet the assumptions for any statistical ... |
So let's say that I am trying to find confidence intervals for the percentage of people who will download a song on a website. We've had 1000 people visit the site in one year and 100 people downloaded the song. Now, I can generate confidence intervals to estimate the expected download rate of visitors to our site.
No... |
If I'm using a machine learning model (e.g. boosted regression trees like gbm in R) on a dataset, what does it mean if there's a significant difference between the OOB estimated optimal # of iterations and the optimal # of iterations on the test set (I'm holding out 20% of the data)?
I ask because I'm trying to model a... |
So let's say I have a bunch of data points in R^n, where n is pretty big (like, 50). I know this data falls into 3 clusters, and I know which cluster each data point is a part of. All I want to do is visualize these clusters in 2D in such a way as to maximize the visual between-clusters separation that I see, with the ... |
Everything I have read has indicated that when performing ANOVA, the null and alternative hypothesis are always the following:
$H_0$: There is no difference in the means,
$H_a$: There is a difference in the means.
But if I have a treatment and I expect, based on past experience or literature, that this treatment woul... |
I have read about controversies regarding hypothesis testing with some commentators suggesting that hypothesis testing should not be used. Some commentators suggest that confidence intervals should be used instead.
What is the difference between confidence intervals and hypothesis testing? Explanation with reference... |
Possible Duplicate:
Assessing error of a spatial interpolation algorithm
This is a similar question to this and this one.
I have a set of 3D points that are sampled from a terrain. The points have three components $x$, $y$, $z$. You can think of these points as the surveyor points that one collects from measuring a... |
Assuming n testers were independently testing the same application for a given period. Each tester found a given set of bugs (Some of the bugs were detected by more than one tester).
For example:
Tester 1 found bugs {1,2,3,4,5} Tester 2 found bugs {3,5,6,7} Tester 3 found bugs {1,3,5,8,9,10}
(The serial number is assi... |
If a one-sided Fisher's exact test testing the null hypothesis that A is not superior to B has a p-value of 0.98, is it true that the Fisher's exact test p-value for the null hypothesis that B is not superior to A is 1-0.98 = 0.02?
The question arises from the paper at nejm.org/doi/full/10.1056/NEJMoa1100403 where the ... |
I used a -4 to +4 Likert scale in one set of questionnaires and -3 to +3 for the same questionnaires, but gathered respondents in a different way. I want to rescale from -4 to +4 down to -3 to +3 for the second group.
How do I do this and secondly is there a referenced/accepted procedure for doing this?
|
Can we say anything about the dependence of a random variable and a function of a random variable? For example is $X^2$ dependent on $X$?
|
I estimate a linear model and then calculate a (White) heteroscedasticity robust variance covariance matrix. This allows me to do the following (where hr.cov is the robust covariance matrix):
> coeftest(model, hr.cov)
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 157.146... |
I have a general question about comparing two studies:
Suppose study $A$ reports a $p$-value less than $0.05$. Also suppose study $B$ reports a $p$-value greater than $0.05$. Assume that both studies have the same $H_0$ and $H_a$. Both studies use different statistical techniques.
Which study is "correct"? Would you ... |
I have a correlation matrix of security returns whose determinant is zero. (This is a bit surprising since the sample correlation matrix and the corresponding covariance matrix should theoretically be positive definite.)
My hypothesis is that at least one security is linearly dependent on other securities. Is there a f... |
I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I go about doing this using SPSS.
|
I'm performing logistic regression for binary classification in SAS and it outputs all of the coefficients to the logit model.
I was wondering how you would take those coefficients and use them to convert the model into a linear hyperplane in the original space (i.e., hyperplane that splits the space into two classes,... |
I'm trying to use SAS from more of a machine learning perspective than a pure stats perspective. I want to perform resampling on a dataset to measure the predictive accuracy of a LDA and Logistic Regression. However, when I perform proc logistic or proc discrim all SAS seems to output is a bunch of statistical measures... |
I've never had a course in statistics, so I hope I'm asking in the right place here.
Suppose I have only two data describing a normal distribution: the mean $\mu$ and variance $\sigma^2$. I want to use a computer to randomly sample from this distribution such that I respect these two statistics.
It's pretty obvious th... |
Suppose I have a list of measurements from an experiment; for example,
34 31 55 18 19 22 44 48 23 . . .
But I then learn that these experiments were conducted by two different technicians, so I embolden those conducted by tech #1, and I leave untouched the measurements of tech #2:
34 31 55 18 19 22 44 48 23 . . .
I... |
Suppose a gambler makes a series of independent bets. In each bet, there's a 50% chance that he loses $\$100$.
If he wins, he has an option to take $\$100$ or run a "winner's bet", instead of taking that reward. In the winner's bet, there is a 60% chance to win 50 dollars, a 30% chance to win 150 dollars, and a 10% to ... |
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