A student shows you a paper copy of these results. Unfortunately, he was caught in a snow shower crossing campus, and only part of the table is readable: X 0 1 p(x) .20 F(x) .33 2 3 4 5 .14 .71 .94 a) Fill in the damaged parts of the table. What is P(1 << 5)? b) Calculate the expected number of pita restaurants, E(X). c) Write down the probability generating function (q) = E(q*). Use it to answer the following question: if 94% of all pita restaurants do takeout, what is the probability that all the pita restaurants in a given town do takeout? (Assume they do not consult each other.)

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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7. A study of a large number of towns with approximately 100,000 people estimates the
probability that one will have a certain number X of pita restaurants. None of the towns had more
Transcribed Image Text:7. A study of a large number of towns with approximately 100,000 people estimates the probability that one will have a certain number X of pita restaurants. None of the towns had more
than 5. They construct a table of the probability distribution function p(x) = P(X = x) and the
cumulative distribution function F(x) = P(X≤x) for the number of pita restaurants in a town.
A student shows you a paper copy of these results. Unfortunately, he was caught in a snow
shower crossing campus, and only part of the table is readable:
X
0
1
p(x)
.20
F(x)
.33
2
.71
3
.14
4
5
.94
a) Fill in the damaged parts of the table. What is P(1 <X< 5)?
b) Calculate the expected number of pita restaurants, E(X).
c) Write down the probability generating function xx(q) = E(q*). Use it to answer the
following question: if 94% of all pita restaurants do takeout, what is the probability that all the
pita restaurants in a given town do takeout? (Assume they do not consult each other.)
Transcribed Image Text:than 5. They construct a table of the probability distribution function p(x) = P(X = x) and the cumulative distribution function F(x) = P(X≤x) for the number of pita restaurants in a town. A student shows you a paper copy of these results. Unfortunately, he was caught in a snow shower crossing campus, and only part of the table is readable: X 0 1 p(x) .20 F(x) .33 2 .71 3 .14 4 5 .94 a) Fill in the damaged parts of the table. What is P(1 <X< 5)? b) Calculate the expected number of pita restaurants, E(X). c) Write down the probability generating function xx(q) = E(q*). Use it to answer the following question: if 94% of all pita restaurants do takeout, what is the probability that all the pita restaurants in a given town do takeout? (Assume they do not consult each other.)
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