Suppose a machines life time in years can be moldeled

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?

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