Question

How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?

score 298 · Answer 1 · 2026-04-03 17:12:11

298

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How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?

Published on 03 Apr 2026 - 17:12

score 270 · Answer 2 · 2026-04-06 05:44:30

270

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Is this a commonly known paradox?

Published on 06 Apr 2026 - 5:44

score 97 · Answer 3 · 2026-04-03 11:48:28

97

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What's $P(A_1\cap A_2\cap A_3\cap A_4) $?

Published on 03 Apr 2026 - 11:48

score 165 · Answer 4 · 2026-04-03 12:07:29

165

Views

Prove or disprove the following inequality

Published on 03 Apr 2026 - 12:07

score 162 · Answer 5 · 2026-04-03 23:37:40

162

Views

Another application of the Central Limit Theorem

Published on 03 Apr 2026 - 23:37

score 125 · Answer 6 · 2026-03-31 16:52:27

125

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Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$

Published on 31 Mar 2026 - 16:52

score 98 · Answer 7 · 2026-04-03 16:50:33

98

Views

A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$

Published on 03 Apr 2026 - 16:50

score 1.7k · Answer 8 · 2026-04-09 19:17:38

1.7k

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proving Kochen-Stone lemma...

Published on 09 Apr 2026 - 19:17

score 145 · Answer 9 · 2026-04-05 11:24:48

145

Views

Solution Check. (Probability)

Published on 05 Apr 2026 - 11:24

score 74 · Answer 10 · 2026-04-03 23:05:47

74

Views

Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process

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score 117 · Answer 11 · 2026-03-29 06:57:14

117

Views

Is there a contradiction in coin toss of expected / actual results?

Published on 29 Mar 2026 - 6:57

score 278 · Answer 12 · 2026-03-30 04:02:00

278

Views

Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$

Published on 30 Mar 2026 - 4:02

score 98 · Answer 13 · 2026-03-30 01:50:46

98

Views

Comparing Exponentials of different rates

Published on 30 Mar 2026 - 1:50

score 67 · Answer 14 · 2026-04-03 15:49:42

67

Views

Sample each point with flipping coin, what is the average?

Published on 03 Apr 2026 - 15:49

score 195 · Answer 15 · 2026-04-09 07:02:44

195

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Linear transform of jointly distributed exponential random variables, how to identify domain?

Published on 09 Apr 2026 - 7:02

List Question

How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?

Is this a commonly known paradox?

What's $P(A_1\cap A_2\cap A_3\cap A_4) $?

Prove or disprove the following inequality

Another application of the Central Limit Theorem

Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$

A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$

proving Kochen-Stone lemma...

Solution Check. (Probability)

Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process

Is there a contradiction in coin toss of expected / actual results?

Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$

Comparing Exponentials of different rates

Sample each point with flipping coin, what is the average?

Linear transform of jointly distributed exponential random variables, how to identify domain?

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