Question: A piece of equipment has a lifetime T (measured in years) that is a continuous random variable with cumulative distribution function
F(t) = 1 - e-t/10 - (t/10) e-t/10 for all t ≥ 0
a. What is the probability density function of T?
b. What is the probability that a piece of equipment survives more than 20 years?
c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years?
d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years?