Question

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

score 110 · Answer 1 · 2026-03-17 11:20:32

110

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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 17 Mar 2026 - 11:20

score 88 · Answer 2 · 2026-03-19 11:56:01

88

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

Published on 19 Mar 2026 - 11:56

score 73 · Answer 3 · 2026-03-24 21:58:38

73

Views

Reason generalized linear model

Published on 24 Mar 2026 - 21:58

score 47 · Answer 4 · 2026-03-22 07:48:05

47

Views

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

Published on 22 Mar 2026 - 7:48

score 195 · Answer 5 · 2026-03-19 19:16:55

195

Views

Variance of a set of quaternions?

Published on 19 Mar 2026 - 19:16

score 996 · Answer 6 · 2026-03-24 15:27:55

996

Views

Is the usage of unbiased estimator appropriate?

Published on 24 Mar 2026 - 15:27

score 41 · Answer 7 · 2026-03-17 11:17:49

41

Views

Stochastic proof variance

Published on 17 Mar 2026 - 11:17

score 105 · Answer 8 · 2026-03-17 19:50:16

105

Views

Bit of help gaining intuition about conditional expectation and variance

Published on 17 Mar 2026 - 19:50

score 247 · Answer 9 · 2026-03-17 15:50:06

247

Views

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

Published on 17 Mar 2026 - 15:50

score 514 · Answer 10 · 2026-03-24 17:08:42

514

Views

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

Published on 24 Mar 2026 - 17:08

score 494 · Answer 11 · 2026-03-20 07:20:48

494

Views

Variance Derivation of Chi-Squared Distribution

Published on 20 Mar 2026 - 7:20

score 1.2k · Answer 12 · 2026-03-19 22:32:01

1.2k

Views

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

Published on 19 Mar 2026 - 22:32

score 103 · Answer 13 · 2026-03-24 20:31:52

103

Views

How is the expression for Bias-Variance obtained?

Published on 24 Mar 2026 - 20:31

score 40 · Answer 14 · 2026-03-25 06:02:06

40

Views

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

Published on 25 Mar 2026 - 6:02

score 1.5k · Answer 15 · 2026-03-20 10:02:28

1.5k

Views

Calculating the Mean and Autocovariance Function of a Piecewise Time Series

Published on 20 Mar 2026 - 10:02

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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