長方形面積S=x(10-x)(0<x<10),
S的數學期望ES=∫<-∞,+∞>Sf(x)dx=∫<0,2>[x(10-x)/2]dx=∫<0,2>[5x-(x^2)/2]dx
=[5(x^2)/2-(x^3)/6]|<0,2>=10-8/6=26/3
ES^2=∫<-∞,+∞>(S^2)f(x)dx=∫<0,2>{(1/2)[x(10-x)]^2}dx=∫<0,2>[50x^2-10x^3+(x^4)/2]dx
=[50(x^3)/3-5(x^4)/2+(x^5)/10]|<0,2>=400/3-40+16/5=1448/15
S的方差DS=E(S-ES)^2=ES^2-(ES)^2=1448/15-(26/3)^2=964/45