Probability Methods for Cost Uncertainty Analysis, 2nd Edition

84 Probability Methods for Cost Uncertainty Analysis

3.23 If a is a constant, show that Markov’s inequality can also be written in

the form P(X ≥ a

1

) ≤ a

−

E(X).

3.24 Let N

W

be a random variable representing the number of widgets pro-

duced in a month. Suppose the expected number of widgets produced

by a manufacturer during a month is 2000.

a. Find an upper bound on the probability this month’s production will

exceed 3200 widgets.

b. Suppose the standard deviation of a month’s production is known

to be 35 widgets. Find a and b such that the number of widgets pro-

duced this month falls in the interval a < N

W

< b with probability

at least