[問題] 三題機率和統計
1. Three fair dice are cast. In 10 independent casts, let
X be the number of times all three faces are alike.
Y be the number of times only two faces are alike.
Find the joint p.d.f. of X and Y and compute E(6XY).
(Ans: E(6XY) = 25/4)
Note: Are X and Y independent?
2. Give a reasonable definition of a chi-square distribution with zero degrees
of freedom.
Hint: Work with the m.g.f. of a distribution that is χ^2(r) and let r = 0.
3. Let X be Poisson distribution with parameter m. If m is an experimental
value of a random variable having a gamma distribution with α = 2 and
β = 1, compute P(X = 0,1,2).
Notation: β = 1 => λ = 1, θ = 1. They're equivalent.
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Thx :)
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◆ From: 218.167.148.187
※ 編輯: ashlem 來自: 218.167.148.187 (08/13 18:10)
※ 編輯: ashlem 來自: 218.167.148.187 (08/13 18:14)
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