Question

In: Statistics and Probability

their respective probabilities as shown below. Number of Breakdowns Probability # of breakdowns Probability 0 .15...

their respective probabilities as shown below.

Number of
Breakdowns


Probability

# of breakdowns Probability
0 .15
1 .41
2 .22
3 .17
4 .04

5 .01

A.) The expected number of machine breakdowns per month

B.) The variance of machine breakdowns per month

C.) The standard deviation of machine breakdowns per month

Solutions

Expert Solution

Solution :

(A)Mean = = X * P(X)

= 0 *0.15 + 1 *0.41 + 2 * 0.22 + 3 * 0.17+ 4 * 0.04+5*0.01

= ( 0+ 0.41 + 0.44 + 0.51+0.16+0.05)

= 1.57

(B)

variance = 2

=X 2 * P(X) - 2

=  [ 02 *0.15 + 12 *0.41 + 22 * 0.22 + 32 * 0.17+ 42 * 0.04+52 *0.01]-1.57

=  [( 0+0.41 + 0.88 + 1.53+0.64+0.25) )] -2.4649

= 3.71 -2.4649

variance = 2 =1.2451

C)Standard deviation =

=X 2 * P(X) - 2

=  [ 02 *0.15 + 12 *0.41 + 22 * 0.22 + 32 * 0.17+ 42 * 0.04+52 *0.01]-1.57

= [( 0+0.41 + 0.88 + 1.53+0.64+0.25) )] -2.4649

= 3.71 -2.4649

=1.2451

Standard deviation = =1.1158

orchestra answered 2 years ago
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