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
dx if x > 0;
what is the probability the system functions for at least 5 months.
Solution. X must be exponential so C is 1
P(X 5) = e- 5
Page 229, n. 4. Suppose X is uniform on (0, 1) and n is a positive integer. Compute E(X) in two
0 if x 0;