let fxk3xx2 if 0 k 3x22 x33 from x0 to x3 k 272 91 k

let f(x)=k(3x-x^2) if 0=<x=< and f(x)=0 if x<0 or x>
for what value of k is f a probability density function and then find the mean

integral (f(x)) from x=0 to 3 should be equal to 1 (probability density function) => k ( 3x^2/2 - x^3/3 ) from x=0 to x=3 k * ( 27/2 - 9)=1 => k= 2/ 9 mean= integral(x f(x) dx) from x=0 to 3 = 2/9 ( x^3 - x^4/4) from x=0 to 3 = 2/9 ( 27- 81/4) = 2/9 * (27/4) =3/2