Notice that if k is an integer, this results in (k)  (k  1)!. If k is not an integer, one must use the recursive definition for (k) coupled with the following table. For values of 1  k2, (k)

is given by k (k) k (k)

1.00 1.0000 1.55 .8889 1.05 .9735 1.60 .8935 1.10 .9514 1.65 .9001 1.15 .9330 1.70 .9086 1.20 .9182 1.75 .9191 1.25 .9064 1.80 .9314 1.30 .8975 1.85 .9456 1.35 .8912 1.90 .9612 1.40 .8873 1.95 .9799 1.45 .8857 2.00 1.0000 1.50 .8862 For example, this table would be used as follows: (3.6)  (2.6)(2.6) 

(2.6)(1.6)(1.6)  (2.6)(1.6)(.8935)  3.717.

a. Compute the expected failure time for Example 13.4 regarding copier equipment.

b. Compute the expected failure time for a piece of operating equipment whose failure law is given in Example 13.2.

c. Determine the mean failure time for   1.35 and   0.20.

d. Determine the mean failure time for   0.90 and   0.45.