已知离散型随机变量x的概率分布为x=0‘1’2‘3,P=0.2,0.1,0.3,a求常数a,x的数学期望EX和方差DX

a=1-0.2-0.1-0.3=0.4
EX=0*0.2+1*0.1+2*0.3+3*0.4=1.9
x^2对应的概率分布为0、1、4、9 P=0.2,0.1,0.3,0.4
EX^2=0*0.2+1*0.1+4*0.3+9*0.4=4.9
DX=EX^2-(EX)^2=4.9-1.9*1.9=1.29