The lifetime in hours Y of an electronic equipment is a rand

The lifetime (in hours) Y of an electronic equipment is a random variable with an exponential distribution with mean 100. Find the probability that the equipment will operate for at least 200 hours without failure.

Solution

For an exponential variable, the cumulative distribution is

F(x) = P(X <x) = 1 - exp(-x/u)

Thus, here,

F(x) = 1 - exp(-x/100)

Thus,

P(x>200) = 1 -F(200) = exp(-200/100) = 0.135335283 [ANSWER]