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### Spearman $\rho$ as a function of Pearson $r$

It is common to talk about the linear correlation, Pearson's $r$, between two random variables $\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$ as having two components: a) the copula and b) the marginal ...
44 views

### How can I generate 2 sets of variables from different distributions with a correlation between them in r? [duplicate]

I am working in R and would like to generate 40 numbers from $\mathrm{N}(0,1)$ and another 40 from $\mathrm{Uniform}(0,2)$ with a negative correlation (for example: $r = -0.45$) between them. The ...
441 views

### Relation between independence and correlation of uniform random variables

My question is fairly simple: let $X$ and $Y$ be two uncorrelated uniform random variables on $[-1,1]$. Are they independent? I was under the impression that two random, uncorrelated variables are ...
186 views

### calculating correlation between binary vectors with generating with uniform distribution

I am working with some correlated binary files. I want to know, what is your opinion for calculating the correlation between binary vectors? for example, if I have two binary vectors X1 and X2 ...
324 views

### how do I draw samples from correlated uniform random variables given a correlation matrix

For a simulation study I am trying to generate samples from 4 correlated random variables following a multivariate uniform distribution, where all marginals are uniform variables and the population ...
275 views

### Generating i.i.d samples in MATLAB: large p-values [duplicate]

I'm trying to generate i.i.d samples from two uniformly distributed random variables in MATLAB. However, when I correlate the two sets of samples, I find that the correlation is almost zero, but the p-...
312 views

### Expectation of 2 functions with one random variable

This may be a trivial question but I want to consult with you all. Let U be a continuous random variable taking values int he interval [0,2pi]. Let X = cos(U), Y = sin(U). Determine the Pearson ...