Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter =0.6. What is (a) the probability that a repair takes less than 8 hours? (b) the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours?

a) 0.9917

b) 0.1652          

Step-by-step explanation:

We are given the following in the question:

The time for repair follows an exponential distribution.

a) P(repair takes less than 8 hours)

0.9917 is the probability that a repair takes less than 8 hours.

b) the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours

thus, 0.1652 is the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours.

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680