.1.5- Every day you consider going jogging. Before each mile, including the first, you will quit with robability q, independent of the number of miles you have already run. However, you are sufficiently lecisive that you never run a fraction of a mile. Also, we say you have run a marathon whenever you un at least 26 miles. (a) Let M equal the number of miles that you run on an arbitrary day. Find the PMF PM(m). (b) Let r be the probability that you run a marathon on an arbitrary day. Find r. (c) Let J be the number of days in one year (not a leap year) in which you run a marathon. Find the PMF P). This answer may be expressed in terms of r found in part (b).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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7.1.5 Every day you consider going jogging. Before each mile, including the first, you will quit with
probability q, independent of the number of miles you have already run. However, you are sufficiently
decisive that you never run a fraction of a mile. Also, we say you have run a marathon whenever you
run at least 26 miles.
(a) Let Mequal the number of miles that you run on an arbitrary day. Find the PMF PM(m).
(b) Let r be the probability that you run a marathon on an arbitrary day. Find r.
(c) Let J be the number of days in one year (not a leap year) in which you run a marathon. Find
the PMF P). This answer may be expressed in terms of r found in part (b).
(d) Define K = M – 26. Let A be the event that you have run a marathon. Find PKJA(k).
Transcribed Image Text:7.1.5 Every day you consider going jogging. Before each mile, including the first, you will quit with probability q, independent of the number of miles you have already run. However, you are sufficiently decisive that you never run a fraction of a mile. Also, we say you have run a marathon whenever you run at least 26 miles. (a) Let Mequal the number of miles that you run on an arbitrary day. Find the PMF PM(m). (b) Let r be the probability that you run a marathon on an arbitrary day. Find r. (c) Let J be the number of days in one year (not a leap year) in which you run a marathon. Find the PMF P). This answer may be expressed in terms of r found in part (b). (d) Define K = M – 26. Let A be the event that you have run a marathon. Find PKJA(k).
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