Re: [商管] [統計]-機率分配
※ 引述《hidmey (:D)》之銘言：
: Two coins are simultaneously tossed until one of them comes up a head
: and the other a tail. The first coin comes up a head with probability 1/3
: and the second with probability 1/2. All tosses are assumed independent.
: Let X be the number of tosses until the game is over.
: 1. Find the expected value and the variance of X
: 2. Given that X is greater than 3, what is the conditional probability
: that X is greater than 5 ?
: 請問這題要用甚麼方向去想呢?
: 本來是想說開離散的機率表
: 但是似乎又不大對
: 麻煩板上高手指點迷津
: 謝謝
第一枚 第二枚 機率
正面 正面 1/6
正面 反面 1/6
反面 正面 1/3
反面 反面 1/3
所以一正一反的機率為p= 1/2 , 第一次成功所需試行的次數為X,則X為幾何分配
f(x)= p(1-p)^(x-1) ,X>=1
所以期望值E(x) = 1/p = 2
變異數V(x) = (1-p)/p^2 = 2
2.幾何分配有無異性質
P(X>5|X>3) = P(X>2) = 1 -P(X=1) - P(X=2)
= 1 - 1/2 - 1/4 = 1/4
※ 編輯: abc911230567 來自: 140.112.22.216 (03/04 15:46)
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03/04 23:16, , 1F
03/04 23:16, 1F
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03/04 23:25, , 2F
03/04 23:25, 2F
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