# Tagged Questions

Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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### Algebraic manipulation of probability distributions

Let $X$ and $Y$ be random vectors that have the same continuous distribution. If $A$ and $B$ are constant matrices and $AX$ and $BY$ have the same distribution does this imply that $A=B$? Are there ...
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### Joint distribution of dependent Bernoulli Random variables

I have $N$ Bernoulli random variables $X_1, ..., X_{N}$ with known parameters $p_1, ..., p_{N}$. I want generate a joint distribution in which these random variables are not independent as I know that ...
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### How to generate multivariate random variables given probability distribution?

Suppose you can generate uniformly distributed random numbers $x_i\in[a,b]$. To shape probability distribution of these numbers as you like using inverse transform sampling. But what if you need to ...
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### How to generate a random variable $r_i$ such that $\sum_{i=1}^n |\frac{r_i}{\sigma_i}|^2\leq\chi^2_{n,\alpha}$

How can I generate $r_i$ for $1 \leq i \leq n$, such that $\sum_{i=1}^n |\frac{r_i}{\sigma_i}|^2\leq\chi^2_{n,\alpha}$, where $\sigma_i^2$ is the variance of $r_i$ and, $\chi^2_{n,\alpha}$ is a chi-...
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### Derive a probability distribution to transform scalars for weighted random sampling

Let's say I have a case with only two choices: $N_a$ = 20 $N_b$ = 10 I want to find a probability distribution that I can map these two values too, such that the probability of one variable being ...
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### Find the PMF for number of heads following the first tail on a four consecutive coin toss expriment

Suppose a fair coin is toss four times consecutively. Find the PMF for random variable of number of heads following the first tail. My take: Let random variable $X$ be the number of heads in this ...