[問題] 一題poisson分配請教
Let X1,X2,X3 be iid Poisson random variable with parameter λ.
Let X4 be a Poisson random variable with parameter 2λ.
Which of the following statements MUST be true?
(a)The statement Cov(X1,X4)=2λ may be true.
(b)E(X1+X4)=3λ
(c)P(X1<X2<X3)=1/6
(d)X2+X4 is a Poisson random variable.
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想請教這題 除了(c)選項是完全不會之外 (b)選項確定對之外
(a)(d)選項只要X1,X2,X3與X4獨立就可以知道答案
但是要怎麼確認X1,X2,X3與X4獨立呢?(一直卡在這裡)
(c)選項 如果題目是continuous r.v.s 答案是1/6
但Poisson是discrete 所以這題該如何做呢?
麻煩版上高手幫忙解救!!
在此先謝謝了^^"
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