设随机变量X,Y相互独立,且服从同一分布,试证明: P{a<min(X,Y)≤b}=...答:【答案】:[证明] 因为X与Y独立同分布,故P{a<min(X ,Y})≤b}=P{min(X,Y)≤b}-P{min(X,Y)≤a},=1-P{min(X,Y)>b}-[1-P{min(X,Y)>a}]=P{min(X,Y)>a}-P{min(X,Y)>b}=P{X>a,Y>a}-P{X>b,Y>b}=P{X>a}P{Y>a}-P{X>b}P{Y>b}=[P{...
设随机变量X与Y相互独立且同分布X的分布律为X=Pk,o=1-p,1=p,令Z=X...答:Z= 0 X=0,Y=0, (1-p)^2 1 X=0,Y=1 or X=1, Y=0, 2p(1-p)2 X=1,Y=1, p^2 E(Z)=0* (1-p)^2+1* 2p(1-p)+2*p^2 =2p D(Z)=E(Z^2)-[E(Z)]^2 =0^2* (1-p)^2+1^2* 2p(1-p)+2^2*p^2-(2p)^2 =2p-2p^2 ...