Summary: Some worked problems from Chapter Five.
Page 228, n. 2. A system consisting of one original unit plus a spare can function for a random amount
of time X. If the density of X is given (in units of months) by
fX(x) = C
xe-x/2
dx if x > 0;
0 else
what is the probability the system functions for at least 5 months.
Solution. X must be exponential so C is 1
2 and
P(X 5) = e- 5
2 .082.
Page 229, n. 4. Suppose X is uniform on (0, 1) and n is a positive integer. Compute E(X) in two
different ways.
Note that
fX(x) =



0 if x 0;

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics