The length of time required by students to complete a exam is a random variable with a density function given by:

f(x) = cx^3 + x if 0 <= x <= 1

0 otherwise

1) find c

2) Find the distribution function F(y).

3) Find the probability that a randomly selected student will finish the exam in less than half an hour

4) Given that a particular student needs at least 0.25 hours to complete the exam. What is the probability Heather will require at least 0.5 hours to complete the exam?

This is what I did:

1) I find the integral from 1 to 0 of x^3 + x

c[(x^4)/4 + (x^2)/2] = 1

c[(1/4) + (1/2) = 1

c(3/4) = 1

c is 4/3.

2)

4/3[(x^4)/4 + (x^2)/2]

[(x^4)/3] + [(2x^2)/3]

Is that correct? What about the rest of the problem? The book doesn't have any example so I am stuck.