5.122 A software engineer models the crashes encountered when executing a new software as a random variable having the Weibull distribution with = 0.06

5.122 A software engineer models the crashes encountered when executing a new software as a random variable having the Weibull distribution with α = 0.06 and β = 6.0. What is the probability that the software crashes after 6 minutes? 5.123 Let the times to breakdown for the processors of a parallel processing machine have joint density f (x, y) =  0.04 e−0.2x−0.2y for x > 0, y > 0 0 elsewhere where x is the time for the first processor and y is the time for the second. Find

(a) the marginal distributions and their means;

(b) the expected value of the random variable whose values are given by g(x, y) = x + y.

(c) Verify in this example that the mean of a sum is the sum of the means.