A consumer organization that evaluates new automobiles custo

A consumer organization that evaluates new automobiles customarily reports the number of major defects in each car examined. Let X denote the number of major defects in a randomly selected car of a certain type. The cdf of X is as follows:

    F(x) =                 

0

0.01

0.24

0.35

0.64

0.87

0.95

1

x < 0

0 ? x < 1

1 ? x < 2

2 ? x < 3

3 ? x < 4

4 ? x < 5

5 ? x < 6

6 ? x

Calculate the following probabilities directly from the cdf:

(a)    p(2), that is, P(X = 2)


(b)    P(X > 3)


(c)    P(2 ? X ? 5)


(d)    P(2 < X < 5)

Solution

(a)    p(2), that is, P(X = 2) =0.35-0.24 = 0.11

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(b)    P(X > 3) =1-0.35 =0.65

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(c)    P(2 <= X <= 5) = 0.95-0.24 = 0.71

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(d)    P(2 < X < 5) = 0.87-0.24 =0.63