Engineering system of type k-out-of-n is operational if at leastk out of n components are operational. Otherwise, the system fails.Suppose that a k-out-of-n system consists of n identical andindependent elements for which the lifetime has Weibulldistribution with parameters r and λ. More precisely, if T is alifetime of a component, P(T ≥ t) = e−λtr, t ≥ 0. Time t is inunits of months, and consequently, rate parameter λ is in units(month)−1. Parameter r is dimensionless. Assume that n = 8,k = 4, r= 3/2 and λ = 1/10. (a) Find the probability that a k-out-of-nsystem is still operational when checked at time t = 3. (b) At thecheck up at time t = 3 the system was found operational. What isthe probability that at that time exactly 5 components wereoperational? Hint: For each component the probability of the systemworking at time t is p = e−0.1 t3/2. The probability that ak-out-of-n system is operational corresponds to the tailprobability of binomial distribution: IP(X ≥ k), where X is thenumber of components working. You can do exact binomialcalculations or use binocdf in Octave/MATLAB (or dbinom in R, orscipy.stats.binom.cdf in Python when scipy is imported). Be carefulwith ≤ and <, because of the discrete nature of binomialdistribution. Part (b) is straightforward Bayes formula.