SOLUTION: Suppose the pdf of the random variable (rv) X is f(x)= c(4x-2x^2) 0＜x＜2, f(x)= 0 otherwise, a) Find c b) Find P(0.5 < X ≤ 1.5).

We have to make the area under the curve from 0 to 2 be 1 unit.
That is, we want the shaded area below to be equal to 1.



So we must find that area, using integration, in terms of c,
set it equal to 1 and solve for c:







We set 

Now that we know c = 3/8, we want to find the shaded area below







Edwin