統計~隨機變數之期望值及變異數

X 0 1 2
f(X) 0.5 0.3 0.2
w 1 4 13
期望值E(X)=0*0.5+1*0.3+2*0.2=0.7
變異數V(X)=E(X^2)-E(X)^2
=0^2*0.5+1^2*0.3+2^2*0.2-0.7^2=0.61
E(X^2)=0^2*0.5+1^2*0.3+2^2*0.2=1.1

期望值E(w)=1*0.5+4*0.3+13*0.2=4.3
變異數V(w)=1^2*0.5+4^2*0.3+13^2*0.2-4.3^2=20.61
E(W)=E(1+3*X^2)=1+3*E(X^2)=1+3*1.1=4.3
V(w)=V(1+3*X^2)=9*V(X^2)=9*2.29=20.61
E(X^4)=0^4*0.5+1^4*0.3+2^4*0.2=3.5
V(X^2)=E(X^4)-E(X^2)^2=3.5-1.1^2=2.29

只是基本練習! 代入定義式計算就成了!