Question

ts) Suppose the demand N is non-negative with mean 15 and that Y = 3N + 7.

(a) What is the best upper bound that you can obtain for P{N > 100}?

(b) Compute E[Y].

(c) If σ 2 denotes the variance of N, what is the variance of Y

Answer 1

(a)

You will have to use the markov's inequality here to get the upperbound of the probability

If X is a nonnegative random variable and a > 0, then the probability that X is at least a is at most the expectation of X divided by a

Thus,

P(N>100) is less than or equal to E(N) / 100 = 15/100 = 0.15

(b)

E(Y) = E(3N+7) = 3*E(N) + 7 = 3*15 + 7 = 52

(c)

Var(Y) = Var(3N+7) = 9*Var(N) = 9*(sigma)^2

Have used the properties of variance and expectation function