随机X、Y同分布,概率密度f(x)={3(x^2)/8 ,0a ,A、B相互独立,且P{AUB}=3/4 ,求a

问题描述:

随机X、Y同分布,概率密度f(x)={3(x^2)/8 ,0a ,A、B相互独立,且P{AUB}=3/4 ,求a

P{AUB}=3/4
则P{A~∩B~}=1-3/4=1/4
即:
p(xA、B相互独立

p(x∫3(x^2)/8dx (0=[x^3/8|x=a]^2
=a^6/64=1/4
则a^6=16
a=4^(1/3)