Suppose a machine's life time ( in years ) can be moldeled with an exponential distribution with rate of lambda = 1/4.
a. What is the proability that the machine will last for at least 7 years, give that it has already last 4 years?
b. What is the mean and variance of this distribution?
c. Suppose 6 of these machines are selected ( each having the same distribution). What is the proability that 2 of them will last at least 3 years?
d. Now suppose we have a batch of 50 such machines. What is the proability that at least 25 will last at least 3 years?