The continuous random variable X has a probability density function f(x) given by f(x)=
⎩
⎨
⎧
k(x
2
−2x+2),
3k,
0,
0 3 otherwise
where k is a constant. (a) Show that k=
9
1
. (b) Find the cumulative distribution function F(x). (c) Find the mean of X.