.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).
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79b73ea4-0228-4ed5-9827-d63c27519cc5%2F023a687d-d741-4bf7-a37f-a3678c15ee8e%2Fzhgf1cji_processed.png&w=3840&q=75)
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