Suppose that f(x)=1.5x^(2) for -1

1 Answers

Best Answer

Let the probability density function f of the random variable X be given as:
f(x)=1.5x^(2), -1<x<1
Calculate:
mathbb(E)(X)=int_(-1)^(1)1.5x^(3)dx=0
mathbb(E)(X^(2))=int_(-1)^(1)1.5x^(4)dx=1.5* (2)/(5)=(3)/(5)
Var(X)=(3)/(5)-0=(3)/(5)
Result:
Mean: 0, Variance: 3/5