List questions from probability-distributions

Published on 11 Apr 2026 - 16:39

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Estimation of unknown mean of a normal distribution

Published on 13 Apr 2026 - 12:55

135

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Why the normal distribution?

Published on 14 Apr 2026 - 4:10

577

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Given a function that generates random numbers with uniform distribution over (0, 1) find a function to generate numbers with Bernoulli distribution.

Published on 12 Apr 2026 - 19:40

113

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Normally distributed conditional random variables

Published on 15 Apr 2026 - 19:31

171

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Strong law of large numbers for a scaled sequence of normally distributed random variables

Published on 26 Mar 2026 - 3:21

141

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Example iid variables $X_i$ where $S=\sum_{j=1}^NX_j$ but $M_S(t) \neq P_N(M_X(t))$

Published on 26 Mar 2026 - 1:17

88

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If $X,Y$ are random variables and $Y\sim\mathcal N(x,\sigma^2)$ if $X=x$, are we able to conclude $Y-X\sim\mathcal N(0,\sigma^2)$?

Published on 17 Apr 2026 - 8:41

69

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Suppose $\frac1{\sqrt{n}}\sum_{i=1}^nY_i\overset{d}\to N(0,V).$ What is the distribution of$\frac1{\sqrt{n}}\sum_{i=1}^nG(Y_i)$?

Published on 15 Apr 2026 - 7:48

186

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Replacing continuous variables in a limit with a sequence

Published on 26 Mar 2026 - 11:34

51

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Distribution of R.V. X given X < Y (or > Y) and Y > constant k

Published on 16 Apr 2026 - 9:31

107

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For part a) am I on the right path? And how do I calculate the probability?

Published on 12 Apr 2026 - 23:52

108

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expectation of the sign of product of bivariate normal variables

Published on 13 Apr 2026 - 23:09

36

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The limiting CDF of a Hypergeometric random variable

Published on 10 Apr 2026 - 17:14

2.6k

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How to calculate probabilities of a football team scoring a certain number of goals

Published on 13 Apr 2026 - 17:55

List Question

Mixing Randomness and Determinism

Estimation of unknown mean of a normal distribution

Why the normal distribution?

Given a function that generates random numbers with uniform distribution over (0, 1) find a function to generate numbers with Bernoulli distribution.

Normally distributed conditional random variables

Strong law of large numbers for a scaled sequence of normally distributed random variables

Example iid variables $X_i$ where $S=\sum_{j=1}^NX_j$ but $M_S(t) \neq P_N(M_X(t))$

If $X,Y$ are random variables and $Y\sim\mathcal N(x,\sigma^2)$ if $X=x$, are we able to conclude $Y-X\sim\mathcal N(0,\sigma^2)$?

Suppose $\frac1{\sqrt{n}}\sum_{i=1}^nY_i\overset{d}\to N(0,V).$ What is the distribution of$\frac1{\sqrt{n}}\sum_{i=1}^nG(Y_i)$?

Replacing continuous variables in a limit with a sequence

Distribution of R.V. X given X < Y (or > Y) and Y > constant k

For part a) am I on the right path? And how do I calculate the probability?

expectation of the sign of product of bivariate normal variables

The limiting CDF of a Hypergeometric random variable

How to calculate probabilities of a football team scoring a certain number of goals

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