Question

Mixing up integrals and expectations with subscript notation

score 79 · Answer 1 · 2026-04-10 20:43:15

79

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Mixing up integrals and expectations with subscript notation

Published on 10 Apr 2026 - 20:43

score 120 · Answer 2 · 2026-03-28 09:50:16

120

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Expected value of $3 \circ 3 \circ 3 \circ \dotsc \circ 3$, with $\circ \in \{+,-,\times,\div\}$

Published on 28 Mar 2026 - 9:50

score 50 · Answer 3 · 2023-05-13 16:03:48

50

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Show that $\sum_{n=1}^\infty P\{X\ge n\}\le EX\le 1+\sum_{n=1}^\infty P\{X\ge n\}$.

Published on 13 May 2023 - 16:03

score 16 · Answer 4 · 2023-05-14 08:18:00

16

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Show that $E(Y)-E(X)=\int_{-\infty}^\infty[P(X<t\le Y)-P(Y<t\le X)]\lambda(dt)$

Published on 14 May 2023 - 8:18

score 27 · Answer 5 · 2023-05-14 09:08:54

27

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Prove that $E(F(X))=\frac{1}{2}+\frac{1}{2}\sum_x[P(X=x)]^2$

Published on 14 May 2023 - 9:08

score 98 · Answer 6 · 2026-03-30 00:22:48

98

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If $X$ follows binomial distribution $B(n,p)$ with $p=\frac1{\sqrt{n}}$, what is the expectation of $\sqrt{X}$.

Published on 30 Mar 2026 - 0:22

score 547 · Answer 7 · 2026-04-03 22:40:15

547

Views

Fair price: receive sum of the last decreasing sequence

Published on 03 Apr 2026 - 22:40

score 45 · Answer 8 · 2023-05-14 17:48:54

45

Views

Prove that $\int_{X>\alpha}XdP\le\alpha(-\log F(\alpha))+\int_\alpha^\infty(-\log F(t))\lambda(dt)$

Published on 14 May 2023 - 17:48

score 158 · Answer 9 · 2026-04-11 02:43:54

158

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Expectation of inverse of the sum of positive random variables

Published on 11 Apr 2026 - 2:43

score 74 · Answer 10 · 2026-04-11 22:12:16

74

Views

How to prove finite absolute value of expectation for $Z(t)=W(t)^2t$ when $W(t)$ is a standard Wiener Process?

Published on 11 Apr 2026 - 22:12

score 35 · Answer 11 · 2026-03-31 05:23:58

finding expectation that involves the indicator function $1_A$ where A is the event $X<l, Y<m$ $X,Y$ are continuous RV. $l,m$ are numbers

score 57 · Answer 12 · 2026-03-31 05:22:50

57

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What is the probability that $\lfloor X/Y \rfloor$ is odd, where $X,Y \sim U(0,1)$?

Published on 31 Mar 2026 - 5:22

score 372 · Answer 13 · 2023-05-17 18:15:55

372

Views

Why Does the Integral of a PDF Equal to the Mean of this Random Variable?

Published on 17 May 2023 - 18:15

score 39 · Answer 14 · 2026-04-11 20:44:05

39

Views

Number of collected coupons until duplicate?

Published on 11 Apr 2026 - 20:44

score 65 · Answer 15 · 2026-04-10 22:44:36

65

Views

100-die ev problem: intuition for strategy

Published on 10 Apr 2026 - 22:44

List Question

Mixing up integrals and expectations with subscript notation

Expected value of $3 \circ 3 \circ 3 \circ \dotsc \circ 3$, with $\circ \in \{+,-,\times,\div\}$

Show that $\sum_{n=1}^\infty P\{X\ge n\}\le EX\le 1+\sum_{n=1}^\infty P\{X\ge n\}$.

Show that $E(Y)-E(X)=\int_{-\infty}^\infty[P(X<t\le Y)-P(Y<t\le X)]\lambda(dt)$

Prove that $E(F(X))=\frac{1}{2}+\frac{1}{2}\sum_x[P(X=x)]^2$

If $X$ follows binomial distribution $B(n,p)$ with $p=\frac1{\sqrt{n}}$, what is the expectation of $\sqrt{X}$.

Fair price: receive sum of the last decreasing sequence

Prove that $\int_{X>\alpha}XdP\le\alpha(-\log F(\alpha))+\int_\alpha^\infty(-\log F(t))\lambda(dt)$

Expectation of inverse of the sum of positive random variables

How to prove finite absolute value of expectation for $Z(t)=W(t)^2t$ when $W(t)$ is a standard Wiener Process?

finding expectation that involves the indicator function $1_A$ where A is the event $X<l, Y<m$ $X,Y$ are continuous RV. $l,m$ are numbers

What is the probability that $\lfloor X/Y \rfloor$ is odd, where $X,Y \sim U(0,1)$?

Why Does the Integral of a PDF Equal to the Mean of this Random Variable?

Number of collected coupons until duplicate?

100-die ev problem: intuition for strategy

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