Probability Density

[rad6210]

Suppose X is a random variable whose density is f(x) = cx(1-x) for 0<x<1, and f(x) = 0 otherwise. Find:
a) the value of c
b) P(X <= 1/2)
c) P(X <= 1/3)

I'm not sure how to do part a), but would part b) be the integral from 0 to 1/2 of cx(1-x) dx , and then solve it that way?
Thanks!

 

[pka]

Suppose X is a random variable whose density is f(x) = cx(1-x) for 0<x<1, and f(x) = 0 otherwise. Find:
a) the value of c
b) P(X <= 1/2)
c) P(X <= 1/3)

\(\displaystyle c = \left( {\int_0^1 {x(1 - x)dx} } \right)^{ - 1}\)