Question

The random variable X has probability density function f(x)={ax+bx2 , 0<x<1 . If E(X)=0.6 , find (a)P(X<1/2) and (b)var(x).

Answer 1

1= integral f(x) dx from 0 to 1 over 1
1= .5 a x^2 + (1/3) b x^3 from 0 to 1
1= .5 a + b/3
and
.6 = E(x) = integral x f(x) dx
.6 = = integral a x^2 + b x^3
.6 = (1/3) a + (1/4) b

solve those two equations for a and b
then you can do f(x) from 0 to 1/2 etc

Answer 2

Answer the question