A mailorder computer business has six telephone lines Let X

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.

Calculate the cdf F(x).

calculate the probabilities of the events given below. (a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}

Solution

a)

Consider the table:

The last column if F(x) here, the asked cdf. [answer]

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b)

Fewer than 3 means at most 2. Hence,

P(fewer than 3) = F(2) = 0.43 [answer]

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c)

P(at least 3) = 1-P(fewer than 3) = 1 - 0.43 = 0.57 [answer]

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d)

As

P(between x1 and x2) = F(x2) - F(x1-1),

P(between 2 and 5) = F(5) - F(2-1) = 0.96-0.25 = 0.71 [ANSWER]