设随机变量X的概率密度为f(x)=cx^2,x>0;0,其他.试求:1常数c;2.E(X),D(X);3.P{|X-E(X)|

问题描述:

设随机变量X的概率密度为f(x)=cx^2,x>0;0,其他.
试求:1常数c;2.E(X),D(X);3.P{|X-E(X)|

(1).1=∫[-∞,+∞]f(x)dx=∫[-2,+2]cx^2dx=16c/3,c=3/16.(2).EX=∫[-2,+2]x*(3/16)x^2dx=(3/16)∫[-2,+2]x^3dx=0.E(X^2)=∫[-2,+2]x^2*(3/16)x^2dx=(3/16)∫[-2,+2]x^4dx=(3/16)*(64/5)=12/5.DX=E(X^2)-(EX)^2=12/5....