[問題] 機率問題 var
想請問一下這一題
The random variables X and Y have joint probability function p(x,y) for x =
0,1 and
y = 0,1,2.
Suppose 3p(1,1) = p(1,2), and p(1,1) maximizes the variance of XY.
Calculate the probability that Xor Y is 0.
(A) 11/25
(B) 23/50
(C) 23/49
(D) 26/49
(E) 14/25
我想假設 Z=XY,p(1,1)=b
0 ｜1-4b
1 ｜b
2 ｜3b
到最後求出
var(Z)=13b-49b^2 有點搞不太懂b與Z的關係
題目的意思是p(1,1)的var是最大值嗎？ 那為何要微分var(Z)？
謝謝
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