Question

Proof that $\mathrm{Var}\bigg(\frac{1}{n} \sum_{i=1}^nY_i\bigg) = \frac{1}{n}\mathrm{Var}(Y_1)$

score 120 · Answer 1 · 2026-05-05 06:14:51

120

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Proof that $\mathrm{Var}\bigg(\frac{1}{n} \sum_{i=1}^nY_i\bigg) = \frac{1}{n}\mathrm{Var}(Y_1)$

Published on 05 May 2026 - 6:14

score 96 · Answer 2 · 2026-05-05 07:08:21

96

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$\{ X_{i} \}_{i=1}^{n} \thicksim iid N(\theta, 1)$. What is distribution of $X_{2} - X_{1}$?

Published on 05 May 2026 - 7:08

score 83 · Answer 3 · 2026-05-05 15:39:58

83

Views

Reason generalized linear model

Published on 05 May 2026 - 15:39

score 55 · Answer 4 · 2026-05-04 13:03:09

55

Views

Variance of $\mathrm{Proj}_{\mathcal{R}(A^T)}(z)$ for $z \sim \mathcal{N}(0, I_m)$.

Published on 04 May 2026 - 13:03

score 212 · Answer 5 · 2026-05-05 12:54:52

212

Views

Variance of a set of quaternions?

Published on 05 May 2026 - 12:54

score 1k · Answer 6 · 2026-05-05 12:32:36

1k

Views

Is the usage of unbiased estimator appropriate?

Published on 05 May 2026 - 12:32

score 54 · Answer 7 · 2026-05-05 06:21:23

54

Views

Stochastic proof variance

Published on 05 May 2026 - 6:21

score 113 · Answer 8 · 2026-05-05 18:10:34

113

Views

Bit of help gaining intuition about conditional expectation and variance

Published on 05 May 2026 - 18:10

score 259 · Answer 9 · 2026-05-05 14:00:33

259

Views

Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$

Published on 05 May 2026 - 14:00

score 529 · Answer 10 · 2026-05-05 13:36:56

529

Views

Compute the variance of $S = \sum\limits_{i = 1}^N X_i$, what did I do wrong?

Published on 05 May 2026 - 13:36

score 500 · Answer 11 · 2026-05-05 10:25:35

500

Views

Variance Derivation of Chi-Squared Distribution

Published on 05 May 2026 - 10:25

score 1.2k · Answer 12 · 2026-05-07 07:43:07

1.2k

Views

Bounding $\text{Var}[X+Y]$ as a function of $\text{Var}[X]+\text{Var}[Y]$

Published on 07 May 2026 - 7:43

score 111 · Answer 13 · 2026-05-07 07:36:52

111

Views

How is the expression for Bias-Variance obtained?

Published on 07 May 2026 - 7:36

score 48 · Answer 14 · 2026-05-07 12:43:15

48

Views

Finding the mean is easy and what about maximizing the variance?

Published on 07 May 2026 - 12:43

score 1.5k · Answer 15 · 2026-05-06 09:54:51

1.5k

Views

Calculating the Mean and Autocovariance Function of a Piecewise Time Series

Published on 06 May 2026 - 9:54

List Question

Proof that $\mathrm{Var}\bigg(\frac{1}{n} \sum_{i=1}^nY_i\bigg) = \frac{1}{n}\mathrm{Var}(Y_1)$

$\{ X_{i} \}_{i=1}^{n} \thicksim iid N(\theta, 1)$. What is distribution of $X_{2} - X_{1}$?

Reason generalized linear model

Variance of $\mathrm{Proj}_{\mathcal{R}(A^T)}(z)$ for $z \sim \mathcal{N}(0, I_m)$.

Variance of a set of quaternions?

Is the usage of unbiased estimator appropriate?

Stochastic proof variance

Bit of help gaining intuition about conditional expectation and variance

Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$

Compute the variance of $S = \sum\limits_{i = 1}^N X_i$, what did I do wrong?

Variance Derivation of Chi-Squared Distribution

Bounding $\text{Var}[X+Y]$ as a function of $\text{Var}[X]+\text{Var}[Y]$

How is the expression for Bias-Variance obtained?

Finding the mean is easy and what about maximizing the variance?

Calculating the Mean and Autocovariance Function of a Piecewise Time Series

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