(2) A mail-order computer business has five telephone lines. Let X denote the nu

Question

(2) A mail-order computer business has five telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of Xis as given in the accompanying table 0 4 x10 1520.25 22 08 Calculate the probability of each of the following events. a. at most 3 lines are in use) b. (fewer than 3 lines are in use) c. at least 3 lines are in use) d. (between 2 and 5 lines, inclusive, are in use) c. between 2 and 4 lines, inclusive, are not in usc) f. fat least 4 lines are not in use) (3) An insurance company offers its policyholders a number of different payment options. For a the number of months between successive payments. The randomly selected policyholder, let X cdf of X is as follows: 0 x

Explanation / Answer

a) P(X<=3) =0.1+0.15+0.2+0.25=0.70

b)P(X<3)=0.1+0.15+0.2=0.45

c)P(X>=3) =1-P(X<3) =1--0.45=0.55

d) P(2<=X<=5) =0.20+0.25+0.22+0.08=0.75

e)=1-P(X<=2<=4)=1-(0.20+0.25+0.22) =0.33

f)=1-P(X>=4)=1-(0.22+0.08)=0.7

3)

from above below is the pmf:

b)

P(3<=X<=6)=0.1+0.05+0.15=0.30

P(X>=4) =1-P(X<4) =1-0.4=0.60

c)

P(X>6) =1-P(X<=6) =1-0.6 =0.40

x f(x) 1 0.3 3 0.1 4 0.05 6 0.15 12 0.4

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