probability density

[mohdsahilali]

Let X be a random variable denotinig the sentence in years for people convicted of a car theft. Suppose max sentence is =3 yrs and probability density function is given by (1/9) . x^2 What is the expected prison sentence after stealing a car?

i need to know how to start going about solving a probability density question!!

[benhur]

here value of X lies between 0 to 3...

f(x) is a pdf.

den E(X)=intregration (limit 0 to 3) {x.f(x)dx}

[Amit Goyal]

as Benhur said you integrate (1/9)x^3 and by putting the limits you get 9/4.