A mail-order computer business has five telephone lines. Let X denote the number
ID: 3206838 • Letter: A
Question
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 X is as given in the accompanying table. Calculate the probability of each of the following events. {at most 3 lines are in use} =_____ {fewer than 3 lines are in use} = _____ {at least 3 lines are in use} = _____ {between 2 and 5 lines, inclusive, are in use} = _____ {at least 4 lines are not in use} = _____ What is the expected value of X? Using the information provided in the table above, what is the edf of X?Explanation / Answer
1)
a) P(X < 3) = 1 - P(X > 3)
= 1 - [P(X = 4) + P(X = 5)]
= 1 - [0.22 + 0.08]
= 0.7
b) P(X < 3) = P(0) + P(1) + P(2)
= 0.10 + 0.15 + 0.2
= 0.45
c) P(X > 3) = 1 - P(X < 3)
= 1 - 0.45
= 0.55
d) P(2 < X < 5) = P(2) + P(3) + P(4) + P(5)
= 0.20 + 0.25 + 0.22 + 0.08
= 0.75
e) P(X < 1) = P(0) + P(1)
= 0.1 + 0.15
= 0.2
2) E(X) = 0 * 0.1 + 1 * 0.15 + 2 * 0.2 + 3 * 0.25 + 4 * 0.22 + 5 * 0.08
= 2.58
3) F(0) = 0.1
F(1) = 0.1 + 0.15 = 0.25
F(2) = 0.25 + 0.20 = 0.45
F(3) = 0.45 + 0.25 = 0.7
F(4) = 0.7 + 0.22 = 0.92
F(5) = 0.92 + 0.08 = 1
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