Question : A continuous random variable has a probability density function

f(x) =

Find the cumulative distribution

find the E[X] and Var X

Solution

The random variable is a uniform distribution random variable

Cumulative Distribution function=

But i dont know how to prove the above ......

My work :

=

= = 0 ...............Is this correct ?

E[X] =

= dx .............What should i do now integrate with and or what

And what about the Var X as well??