The total time, measure in units of 100 hours, that a teenager runs her stero set over a period of one year is a continuous random variable X that has the density function:
f(x) = x, 0<x<1
Evalue the mean of the random variable Y=60X^2 + 39X , where Y is equal to the number of kilowatt hours expended annually.
what i did was :
E(X) = int 0-1 x dx + int 1-2 (2-x) dx
E(X^2) = int 0-1 X^2 dx + int 1-2 x(2-x) dx
and then E(Y) = 60((EX^2)) + 39 (E(X))
but it doesn't add up to 109 (answer)
what did i do wrongly ?