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
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.
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.