Question

随机变量x的分布率当x=-1时p=0.3,当x=0时p=0.4,当x=2时,p=0.3,求期望和方差

Answer 1

期望为P

P=-1*0.3+0*0.4+2*0.3=-0.3+0.6=0.3

方差公式为：S^ 2=1/n[(x1-m)^2+(x2-m)^2+...+(xn-m)^2]

所以该题的方差为：

S^ 2=(1/3)*[(x1-P)^2+(x2-P)^2+(x3-P)^2]

=0.33*[(-1-0.3)^2+(0-0.3)^2+(2-0.3)^2]

=0.33*(1.69+0.09+2.89)

=0.33*4.67

=1.5411.

所以期望为0.3,方差为1.5411.