推 ethan0221 :感謝! :] 05/05 10:03
※ 引述《ethan0221 (Ethan)》之銘言：
: 題目如下:
: Let U be a uniform random variable on interval(0,1). Suppose that the
: conditional distribution of X, given U = p, is binomial with parameter(n,p).
: Find the probability mass function of X.
: 感謝回答! :]
f(x,p)=C(n,x)p^x(1-p)^(n-x), x=0,...,n, 0<p<1
1 n! x!(n-x)!
f(x)=∫ f(x,p)dp=C(n,x)beta(x+1,n-x+1)=--------- ----------
0 x!(n-x)! (n+1)!
=1/(n+1), x=0,...,n
so X is discete uniform distribution
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