List questions from probability-distributions

Published on 16 Apr 2026 - 16:18

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This is a probability mass function problem

Published on 10 Apr 2026 - 16:41

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Probability excersice

Published on 12 Apr 2026 - 20:54

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If $ X = \sqrt{Y_{1} Y_{2}} $, then find a multiple of $ X $ that is an unbiased estimator for $ \theta $.

Published on 14 Apr 2026 - 21:04

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Marginal Density Question

Published on 13 Apr 2026 - 9:08

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show that MSE$(\hat{\theta}) = E[(\hat{\theta} − θ)^2] = V(\hat{\theta}) + (B(\hat{\theta}))^2$.

Published on 15 Apr 2026 - 18:34

93

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Exponential distribution of runners

Published on 09 Apr 2026 - 5:34

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If $S'^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n}$ and $S^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n-1}$, find $V(S'^2)$.

Published on 16 Apr 2026 - 7:29

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Prove that the usual (1-$\alpha$)% confidence interval for $\sigma^2$ is NOT the shortest interval.

Published on 13 Apr 2026 - 17:25

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Let $Y,Z$ be idd. RV's, $\ Z \sim e(1), \ Y \sim R(0,1)$. Find $f_{X,Y}$ for $(X,Y)$.

Published on 16 Apr 2026 - 14:53

78

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How to evaluate this expectation value?

Published on 10 Apr 2026 - 7:39

4.1k

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If X and Y are equal almost surely, then they have the same distribution, but the reverse direction is not correct

Published on 15 Apr 2026 - 18:56

2.1k

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Expected value of 2 Poisson distributions

Published on 09 Apr 2026 - 23:12

363

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Conditional Expectation Problem With Noise

Published on 09 Apr 2026 - 1:04

711

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what value for $c$ yields the estimator for $σ^2$ with the smallest mean square error among all estimators of ....

Published on 10 Apr 2026 - 21:24

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Exchangeability of a Joint PDF

This is a probability mass function problem

Probability excersice

If $ X = \sqrt{Y_{1} Y_{2}} $, then find a multiple of $ X $ that is an unbiased estimator for $ \theta $.

Marginal Density Question

show that MSE$(\hat{\theta}) = E[(\hat{\theta} − θ)^2] = V(\hat{\theta}) + (B(\hat{\theta}))^2$.

Exponential distribution of runners

If $S'^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n}$ and $S^2 = \frac{\sum_{i=1}^n (Y_i - \bar{Y})^2}{n-1}$, find $V(S'^2)$.

Prove that the usual (1-$\alpha$)% confidence interval for $\sigma^2$ is NOT the shortest interval.

Let $Y,Z$ be idd. RV's, $\ Z \sim e(1), \ Y \sim R(0,1)$. Find $f_{X,Y}$ for $(X,Y)$.

How to evaluate this expectation value?

If X and Y are equal almost surely, then they have the same distribution, but the reverse direction is not correct

Expected value of 2 Poisson distributions

Conditional Expectation Problem With Noise

what value for $c$ yields the estimator for $σ^2$ with the smallest mean square error among all estimators of ....

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