作者buttermilk (脱脂牛奶)
看板Statistics
标题[问题] 一题求变异数的问题
时间Mon Oct 30 20:16:14 2006
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) 我会算 )
(b) Give the values of the mean, variance, and standard deviation of X.
Ans: μ = 3, σ^2 = 2, σ = 1.414
( σ^2我不会算，所以σ也不会算 )
(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)我也会算 )
请问σ^2 = 2要怎麽算，用定义我算不出来
要用动差母函数的 M'(0) 和 M''(0) 吗？ ( σ^2 = M''(0) - [M'(0)]^2 )
用动差母函数我好像也算不出来耶@@
还是要用负二项分配 ( negative binomial distribution ) 算 ？
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