Suppose a continuous random variable Z has probability density function f(Z) = bZ for 0 ≤ Z ≤ 3 and f(Z) = 0 for Z < 0 and Z > 3.
1.Compute the constant b.
2.Find Prob(Z < 1).
3.Find Prob(Z > 2.5)
Hint: Start by plotting the pdf, which is obviously an upward sloping line coming out of the origin.