# Thread: Unusual random variable density function

1. ## Unusual random variable density function

A random variable X has the density function a*sin(x) + b*cos(x), if 0 < x < pi/2

Find 'a' and 'b'

2. Sorry, I forgot to include a piece of information relevant to the problem: E(X) = 1/3 + pi/6

3. Originally Posted by DannyOcean
A random variable X has the density function a*sin(x) + b*cos(x), if 0 < x < pi/2

Find 'a' and 'b'
Surely you would try get two equation in a and b from:

$\int_0^{\pi/2} f(x) \, dx = 1$ and $E(X) = \int_0^{\pi/2} x f(x) \, dx$

and then solve them simultaneously.