A mail-order computer business has six telephone lines. Let X denote the number

Question

A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table 0 1 2345 6 P(x) 0.12 0.18 0.20 0.20 0.20 0.06 0.04 Calculate the cdf Fx) F(x) Graph the cdf Fx) F(x) F(x) 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 1 2 345 6 7 1 2 345 6 7 F(x) F(x) 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 1 2 345 6 7 1 2 345 6 7 Use the graph to calculate the probabilities of the events given belovw. (a) at most three lines are in usel (b) ffewer than three lines are in use) (c) at least three lines are in use) (d) (between two and five lines, inclusive, are in use)

Explanation / Answer

from above below is CDF:

for graph of CDF : top left curve is right

a)P(at most 3 lines) =P(X<=3) =0.7

b)P(X<3) =0.5

c)P(X>=3)=1-P(X<=2)=0.5

d) P(2<=X<=5)=0.66

x 0 1 2 3 4 5 6 F(x) 0.12 0.3 0.5 0.7 0.9 0.96 1

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