The random variable x is uniformly distributed over the inte

The random variable x is uniformly distributed over the interval (5,10)

a) if y = G(x) = 4x² find f_y(y)

b) Determine E{G(x)}

Solution

a) y = 4*x^2

Then, fy(y) = 1/ [20* sqrt(y) ] when 100< y <400.............

   = 0 otherwise.............

b) E(G(x) ) = E( 4x2 ) = 4 E(x2 ) =4 [ var(x) + ( E(x) ) ^2 ] = 4 [ 25/12 + (7.5)^2 ] = 233.3333.....