Let X equal the number of flips of a fair coin that are required to
observe the same face on consecutive flips.
(a) Find the p.m.f of X.
Ans: f(x) = (1/2)^(x-1) , x = 2,3,4,‥‥‥ ( (a) 我會算 )
(b) Give the values of the mean, variance, and standard deviation of X.
Ans: μ = 3, σ^2 = 2, σ = 1.414 ( σ^2我不會算，所以σ也不會算 )
(c) Find the values of (i) P ( X≦3 ) , (ii) P ( X≧5 ) , (iii) P ( X=3 )
Ans: (i) 3/4, (ii) 1/8, (iii) 1/4 ( (c)我也會算 )
請問σ^2 = 2要怎麼算，用定義我算不出來
要用動差母函數的 M'(0) 和 M''(0) 嗎？ ( σ^2 = M''(0) - [M'(0)]^2 )
用動差母函數我好像也算不出來耶@@
還是要用負二項分配 ( negative binomial distribution ) 算 ？
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