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设随机变量X的概率分布为：P(X=k)=1/2^k(k=1,2,3,…)求：1).P{X为偶数}2).P{X>=5}解：1) P{X为偶数}=P{x=2}+ P{x=4}+ P{x=6}+ P{x=8}+…=1/2^2+1/2^4+1/2^6+1/2^8+…=1/4+1/4^2+1/4^3+1/2^4+…=(1/4)/(1-1/4)=1/32) P{X>=5}=P{x=5}+ P{x=6}+ P{x=7}+ P{x=8}+…=1/2^5+1/2^6+1/2^7+1/2^8+…=(1/2^5)/(1-1/2)=1/16或P{X>=5}=1- P{X<5}=1- P{x=1}- P{x=2}- P{x=3}- P{x=4}=1-1/2-1/4-1/8-1/16=1/16[@more@]