Question

Prove homogeneity of cumulants: If a random variable X is independent, show $\kappa_n(\alpha X) = \alpha^n \kappa_n(X)$

score 87 · Answer 1 · 2026-04-09 08:09:50

87

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Prove homogeneity of cumulants: If a random variable X is independent, show $\kappa_n(\alpha X) = \alpha^n \kappa_n(X)$

Published on 09 Apr 2026 - 8:09

score 23 · Answer 2 · 2026-04-11 11:05:20

23

Views

Show the following expected value holds true

Published on 11 Apr 2026 - 11:05

score 71 · Answer 3 · 2026-04-01 09:54:40

71

Views

Calculate $\operatorname{Cov}(X, X^2)$ for $X \sim N(\mu, \mu^2)$

Published on 01 Apr 2026 - 9:54

score 65 · Answer 4 · 2023-04-25 00:06:12

65

Views

Expected Value of the number of 0's and 1's until a certain pattern occur

Published on 25 Apr 2023 - 0:06

score 74 · Answer 5 · 2023-04-25 03:13:29

74

Views

$X_n\to \textrm{Exp}(5)$ and $Y_n\to 10$ in distribution. To what does $E[X_n Y_n]$ converge?

Published on 25 Apr 2023 - 3:13

score 124 · Answer 6 · 2023-04-25 10:26:35

124

Views

Expectation of almost surely finite sum

Published on 25 Apr 2023 - 10:26

score 95 · Answer 7 · 2023-04-26 08:02:52

95

Views

Weighted sum of i.i.d. random variables

Published on 26 Apr 2023 - 8:02

score 85 · Answer 8 · 2023-04-26 12:19:17

85

Views

Why is $E[X_{A \text{ or } B}]$ equal to half the harmonic mean of $E[X_A]$ and $E[X_B]$?

Published on 26 Apr 2023 - 12:19

score 118 · Answer 9 · 2026-03-26 12:52:13

118

Views

Compound Poisson Distribution and its Expected Value

Published on 26 Mar 2026 - 12:52

score 369 · Answer 10 · 2026-03-25 13:56:23

369

Views

E[XY] where X and Y are the sign functions of standard normal distributions

Published on 25 Mar 2026 - 13:56

score 41 · Answer 11 · 2023-04-26 22:06:22

41

Views

Mean value of $Z = \min(X, M)$, where $M$ is a positive constant

Published on 26 Apr 2023 - 22:06

score 41 · Answer 12 · 2026-03-31 01:08:38

41

Views

Decomposing a uniform discrete random variable

Published on 31 Mar 2026 - 1:08

score 43 · Answer 13 · 2026-04-11 09:31:53

43

Views

Find the expectation of a complex random variable.

Published on 11 Apr 2026 - 9:31

score 63 · Answer 14 · 2023-04-27 08:36:57

63

Views

Expected value of $XY$ and $X^2Y^2$ for discrete and not independent random variables

Published on 27 Apr 2023 - 8:36

score 61 · Answer 15 · 2026-04-11 16:57:34

61

Views

property of expectation when $\Bbb{Q} \ll \Bbb{P}$

Published on 11 Apr 2026 - 16:57

List Question

Prove homogeneity of cumulants: If a random variable X is independent, show $\kappa_n(\alpha X) = \alpha^n \kappa_n(X)$

Show the following expected value holds true

Calculate $\operatorname{Cov}(X, X^2)$ for $X \sim N(\mu, \mu^2)$

Expected Value of the number of 0's and 1's until a certain pattern occur

$X_n\to \textrm{Exp}(5)$ and $Y_n\to 10$ in distribution. To what does $E[X_n Y_n]$ converge?

Expectation of almost surely finite sum

Weighted sum of i.i.d. random variables

Why is $E[X_{A \text{ or } B}]$ equal to half the harmonic mean of $E[X_A]$ and $E[X_B]$?

Compound Poisson Distribution and its Expected Value

E[XY] where X and Y are the sign functions of standard normal distributions

Mean value of $Z = \min(X, M)$, where $M$ is a positive constant

Decomposing a uniform discrete random variable

Find the expectation of a complex random variable.

Expected value of $XY$ and $X^2Y^2$ for discrete and not independent random variables

property of expectation when $\Bbb{Q} \ll \Bbb{P}$

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