The length of time required by students to complete a 1 hour exam is a random variable with a density function given by:
f(y) = cy^2 + y for o<= y <= 1
and 0 elsewhere

a. Find c

b. Find the cumulative distribution function for this random variable F(y)

c. Find P( 0<= Y <= .5)

d. Find P( Y > .5 | Y > .1)

e. Find the expected value for Y