List questions from probability-distributions

Published on 13 Apr 2026 - 16:08

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Derive the Cramer-Rao lower bound (CRLB) for the variance of any unbiased for estimator of $\lambda$ for random sample from Poisson ($\lambda$)

Published on 15 Apr 2026 - 9:37

285

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Show $E(\frac{1}{2\theta\sum_{i = 1}^n W_i}) = \frac{1}{2(n-1)}$ given the pdf $f(y\mid\theta) = \theta y^{\theta - 1}$

Published on 14 Apr 2026 - 23:59

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Show that $S = \sqrt{S^2}$ is a biased estimator of $\sigma$ given a random sample from a normal distribution ...

Published on 11 Apr 2026 - 20:46

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How to use the Cramer-Rao lower bound (CRLB)to show that $\bar{Y}$ is the best unbiased estimator of $\lambda$?

Published on 12 Apr 2026 - 17:31

1.6k

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Expected value of multiple random variables, uniform distribution

Published on 11 Apr 2026 - 23:12

261

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Marginal PDF integral not converging

Published on 14 Apr 2026 - 10:16

59

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independence - joint distribution

Published on 10 Apr 2026 - 20:12

216

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Average minimum distance

Published on 12 Apr 2026 - 21:16

178

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Using continuity correction for normal distribution

Published on 12 Apr 2026 - 0:34

63

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Distrbution of Matrix times vector

Published on 15 Apr 2026 - 18:27

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Normalization for Chi square test

Published on 11 Apr 2026 - 10:15

111

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Convergence of the probability of a R.V.

Published on 15 Apr 2026 - 15:07

96

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Asymptotic marginals of uniformly-distributed simplex

Published on 16 Apr 2026 - 3:34

1k

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An Application of the Neyman-Pearson Lemma.

Published on 11 Apr 2026 - 10:48

List Question

Chi square distribution vs. Chi square test

Derive the Cramer-Rao lower bound (CRLB) for the variance of any unbiased for estimator of $\lambda$ for random sample from Poisson ($\lambda$)

Show $E(\frac{1}{2\theta\sum_{i = 1}^n W_i}) = \frac{1}{2(n-1)}$ given the pdf $f(y\mid\theta) = \theta y^{\theta - 1}$

Show that $S = \sqrt{S^2}$ is a biased estimator of $\sigma$ given a random sample from a normal distribution ...

How to use the Cramer-Rao lower bound (CRLB)to show that $\bar{Y}$ is the best unbiased estimator of $\lambda$?

Expected value of multiple random variables, uniform distribution

Marginal PDF integral not converging

independence - joint distribution

Average minimum distance

Using continuity correction for normal distribution

Distrbution of Matrix times vector

Normalization for Chi square test

Convergence of the probability of a R.V.

Asymptotic marginals of uniformly-distributed simplex

An Application of the Neyman-Pearson Lemma.

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