Question

Trying to find the conditional expected value of X when X + Y = m, and X, Y are both independent binomial random variables w/ parameters n & p

score 1k · Answer 1 · 2020-12-10 05:17:25

1k

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Trying to find the conditional expected value of X when X + Y = m, and X, Y are both independent binomial random variables w/ parameters n & p

Published on 10 Dec 2020 - 5:17

score 70 · Answer 2 · 2020-12-10 21:13:45

70

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$0^2{{n}\choose{0}} + 1^2{{n}\choose{1}} + 2^2 {{n}\choose{2}} + ... +n^2{{n}\choose{n}} = n (1+n)* 2^{n-2}, n \in \mathbb{N} \setminus \{0\}$ proof.

Published on 10 Dec 2020 - 21:13

score 124 · Answer 3 · 2020-12-11 01:56:37

124

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How can I prove binomial identities using the Binomial Theorem?

Published on 11 Dec 2020 - 1:56

score 116 · Answer 4 · 2026-04-03 15:51:23

116

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Estimating values using the binomial theorem trivial

Published on 03 Apr 2026 - 15:51

score 42 · Answer 5 · 2020-12-12 14:27:33

42

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Binomial series differential equation

Published on 12 Dec 2020 - 14:27

score 61 · Answer 6 · 2020-12-13 08:17:46

61

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Show that $(n+1)^{n-1}<n^n$ using the binomial theorem

Published on 13 Dec 2020 - 8:17

score 152 · Answer 7 · 2020-12-14 08:51:49

152

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Factorization of $a^{n}-b^{n}$.

Published on 14 Dec 2020 - 8:51

score 89 · Answer 8 · 2020-12-14 11:10:27

89

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A question of Number Theory+Binomial Theorem

Published on 14 Dec 2020 - 11:10

score 123 · Answer 9 · 2020-12-14 17:51:37

123

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$101$-th power of three-digit integer $n$ ends with the same three digits of $n$

Published on 14 Dec 2020 - 17:51

score 114 · Answer 10 · 2026-03-25 17:39:45

114

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Number comparison: $5^{152}<2^{353}$ and $2^{1413}<3\cdot 5^{608}$

Published on 25 Mar 2026 - 17:39

score 14 · Answer 11 · 2020-12-15 11:57:00

14

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Simplifying equation with fraction powers

Published on 15 Dec 2020 - 11:57

score 335 · Answer 12 · 2026-04-03 01:01:57

335

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What is probability that jury returns correct decision for the trial that you attend?

Published on 03 Apr 2026 - 1:01

score 121 · Answer 13 · 2020-12-19 22:20:51

121

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Give a combinatorial argument to evaluate sum $\sum_{k}^{n}\binom{n }{k}\binom{m}{k}$

Published on 19 Dec 2020 - 22:20

score 75 · Answer 14 · 2020-12-21 06:33:22

75

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Greatest value of $n^{1/n}$ without calculus where n is a natural number.

Published on 21 Dec 2020 - 6:33

score 60 · Answer 15 · 2020-12-23 18:44:10

60

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How did this shorter method of finding $x^r$ in equation come?

Published on 23 Dec 2020 - 18:44

List Question

Trying to find the conditional expected value of X when X + Y = m, and X, Y are both independent binomial random variables w/ parameters n & p

$0^2{{n}\choose{0}} + 1^2{{n}\choose{1}} + 2^2 {{n}\choose{2}} + ... +n^2{{n}\choose{n}} = n (1+n)* 2^{n-2}, n \in \mathbb{N} \setminus \{0\}$ proof.

How can I prove binomial identities using the Binomial Theorem?

Estimating values using the binomial theorem trivial

Binomial series differential equation

Show that $(n+1)^{n-1}<n^n$ using the binomial theorem

Factorization of $a^{n}-b^{n}$.

A question of Number Theory+Binomial Theorem

$101$-th power of three-digit integer $n$ ends with the same three digits of $n$

Number comparison: $5^{152}<2^{353}$ and $2^{1413}<3\cdot 5^{608}$

Simplifying equation with fraction powers

What is probability that jury returns correct decision for the trial that you attend?

Give a combinatorial argument to evaluate sum $\sum_{k}^{n}\binom{n }{k}\binom{m}{k}$

Greatest value of $n^{1/n}$ without calculus where n is a natural number.

How did this shorter method of finding $x^r$ in equation come?

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