Consider a random variable Y gX where Y 5 X SolutionTo fin

Consider a random variable Y = g(X) where Y= { -5, X

Solution

To find the density function f_Y(y) of Y, one strategy is to find the cumulative distribution functionF_Y(y), and then differentiate.

Note that Y is always positive in y >=0, so F_Y(y)=0 if y0. Now suppose that y>0. Then

F_y(y) = integral ( 0->y) xdx

= (0->y) x^2/2

= y^2/2

Therefore ,

PDF = y