Calculating P(X<0.5) and V(x) for r.v. X with pdf f(x) = ax + bx^2 0<x<1

[TomJerry]

Question:
The r.v. X has pdf f(x) = ax + bx^2 0<x<1
0 otherwise

If E(x) = 0.6 , find
i) P(X<0.5)
ii) V(x)

Solution:
E(x) =0.6 = \mu

Stuck here

 

[statdad]

You know two things:

<br /> \int_0^1 f(x)\, dx = 1, \quad \int_0^1 xf(x)\,dx = .6<br />

These let you find the coefficients, and then you finish the solution.