Question: For the equipment mentioned in Problem,
a. Derive the failure rate function r(t), and draw a graph of the function.
b. Without using the failure rate function, determine the probability that a piece of equipment that has survived 20 years of operation fails in the 21st year.
c. Does r(20) accurately estimate your answer to part (b)? Why or why not?
Problem: 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?