2022-11-26

A customer organization that evaluates new automobiles customarily reports the
number of major defects in each car examined. Let ܺ denote the number of major
defects in a randomly selected car of a certain type. The cdf of ܺ is as follows:
= (ݔ)ܨ
ە
ۖ
ۖ
۔
ۖ
ۖ
ۓ
0 if ݔ > 0
0.06 if 0 ≤ ݔ > 1
0.19 if 1 ≤ ݔ > 2
0.39 if 2 ≤ ݔ > 3
0.67 if 3 ≤ ݔ > 4
0.92 if 4 ≤ ݔ > 5
0.97 if 5 ≤ ݔ > 6
1 if 6 ≤ ݔ
Calculate the following probabilities directly from the cdf.
a. ܲ(ܺ = 2)
b. ܲ(ܺ > 3)
c. ܲ(2 ≤ ܺ ≤ 5)
d. ܲ(2 < ܺ < 5)

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