List questions from normal-distribution

Published on 02 Feb 2019 - 16:41

50

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Why do we have to standardize first?

Published on 03 Feb 2019 - 8:48

54

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Any good approximation for $\Phi^{-1}(1-\Phi(a))$?

Published on 25 Mar 2026 - 9:53

64

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Chi-squared distribution problem

Published on 26 Mar 2026 - 1:09

93

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Probabilty Distribution of M objects moving in circular grid with N positions

Published on 25 Mar 2026 - 18:55

165

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Limit of a Symmetric Random Walk

Published on 25 Mar 2026 - 23:09

106

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Expectation of ratio of normal and root chi-square

Published on 27 Mar 2026 - 8:56

68

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Example of $X,Y$ normal ditributed s.t. $\mathbb E[XY]=\mathbb E[Y]\mathbb E[Y]$ but $X$ and $Y$ are not independent.

Published on 05 Feb 2019 - 20:34

77

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Moment generating functions and normal distributions

Published on 30 Mar 2026 - 15:39

138

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If $X_1,X_2 \sim N(\mu,\sigma^2)$ , then find $E[(X_1+X_2)^2|X_1=X_2]$

Published on 29 Mar 2026 - 4:44

136

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Compute $\mathbb{E}(2X_1+3X_2\mid X_1+3X_2-X_3=4)$ for $(X_k)$ i.i.d standard normal

Published on 29 Mar 2026 - 10:37

238

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Assume that $Z_i\sim\mathcal{N}(0,1)$ are independent and prove that $\sum\limits_{i=1}^{n}(Z_i-\overline{Z})^{2}\sim\chi^{2}_{(n)}$

Published on 29 Mar 2026 - 22:34

448

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Show that $(X,Y)$ has bivariate normal distribution when $X = Z_{1}$ and $Y = Z_{1} + Z_{2}$, where $Z_{i}\sim\mathcal{N}(0,1)$

Published on 25 Mar 2026 - 14:25

208

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Arriving at Maximum Likelihood Estimates

Published on 22 Mar 2026 - 22:26

225

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Calculating the convolution of an Arcsine law and a Gaussian distribution

Published on 07 Feb 2019 - 14:28

List Question

Normal Distribution Quantiles - Is my solution correct?

Why do we have to standardize first?

Any good approximation for $\Phi^{-1}(1-\Phi(a))$?

Chi-squared distribution problem

Probabilty Distribution of M objects moving in circular grid with N positions

Limit of a Symmetric Random Walk

Expectation of ratio of normal and root chi-square

Example of $X,Y$ normal ditributed s.t. $\mathbb E[XY]=\mathbb E[Y]\mathbb E[Y]$ but $X$ and $Y$ are not independent.

Moment generating functions and normal distributions

If $X_1,X_2 \sim N(\mu,\sigma^2)$ , then find $E[(X_1+X_2)^2|X_1=X_2]$

Compute $\mathbb{E}(2X_1+3X_2\mid X_1+3X_2-X_3=4)$ for $(X_k)$ i.i.d standard normal

Assume that $Z_i\sim\mathcal{N}(0,1)$ are independent and prove that $\sum\limits_{i=1}^{n}(Z_i-\overline{Z})^{2}\sim\chi^{2}_{(n)}$

Show that $(X,Y)$ has bivariate normal distribution when $X = Z_{1}$ and $Y = Z_{1} + Z_{2}$, where $Z_{i}\sim\mathcal{N}(0,1)$

Arriving at Maximum Likelihood Estimates

Calculating the convolution of an Arcsine law and a Gaussian distribution

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