probability help please?

Question

A continuous random variable X has probability density function (pdf):
fX(x) =
0 if x < 1
2(x−1) if 1 <= x <= 2
0 if x > 2
Find the cdf of X.
Calculate E(X), E(X^2), E(X^3), Var(X) and the median of X.
(<=means smaller or equal)

Answer 1

The cdf is simply the integral of the pdf.

You can integrate 2x-2 over x from 1 to 2 , right?

Those other expressions are obtained by using the definitions and doing the integrals

E(x) = int x=1 to 2 { x*pdf(x)}

Note that pdf = 0 for x<1 and x>2 so doesn't enter the integrations

similar expressions must be evaluated for the others.

Your pdf is a linear function, so for E(x^3) you just have to do a 4th order polynomial, which is not difficult.

Post your partial answers and I'll check them if you want.