The number of failures of a computer system in a week of operation has the following probability distribution: No of failures Probability0 0.181 0.282 0.253 0.184 0.065 0.046 0.01Find the expected value of the number of failures that will occur next week.

1.82

Explanation:

No of Failures                 Probability

   0                                         0.18

   1                                          0.28

   2                                         0.25

   3                                         0.18

   4                                        0.06

   5                                        0.04

   6                                        0.01

EV of Number of failures = ∑ N*P(N)

where p = probability of occurrence

and n = no of failures

The expected value is the sum of all the failures multiplied by their individual probabilities

EV = (0*0.18) + (1 * 0.28) + (2 * 0.25) + (3 * 0.18) + (4 * 0.06) + (5 * 0.04) + (6 * 0.01)

= 0 + 0.28 + 0.5 + 0.54 + 0.24 + 0.2 + 0.06

= 1.82