3. Sir Harold Jeffreys, doesn't like the way Fisher teaches statistics and decides to teach a class on 'Bayesian Statistics'. Toward the end of the quarter, he also asks his students to form teams of 1 to 4 individuals to work on a group project. Let Y be the team size for a specific group project in Jeffreys' class. The following table shows the cdf of Y: 1 3 4 P(Y < y) 0.12 0.38 0.75 1 (a) What is the probability that a team has two students in Jeffreys' class? (b) Compute the probability that a team in Jeffreys' class has at least 2 students. Compared to Fisher's from question 2, which class has a higher probability of having teams of at least two students? (c) Compute the expected team size in Jeffreys' class. Is it greater than the expected team size in Fisher's class?
3. Sir Harold Jeffreys, doesn't like the way Fisher teaches statistics and decides to teach a class on 'Bayesian Statistics'. Toward the end of the quarter, he also asks his students to form teams of 1 to 4 individuals to work on a group project. Let Y be the team size for a specific group project in Jeffreys' class. The following table shows the cdf of Y: 1 3 4 P(Y < y) 0.12 0.38 0.75 1 (a) What is the probability that a team has two students in Jeffreys' class? (b) Compute the probability that a team in Jeffreys' class has at least 2 students. Compared to Fisher's from question 2, which class has a higher probability of having teams of at least two students? (c) Compute the expected team size in Jeffreys' class. Is it greater than the expected team size in Fisher's class?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![3. Sir Harold Jeffreys, doesn’t like the way Fisher teaches statistics and decides to teach a class on ‘Bayesian Statistics’. Toward the end of the quarter, he also asks his students to form teams of 1 to 4 individuals to work on a group project. Let \( Y \) be the team size for a specific group project in Jeffreys’ class. The following table shows the cdf of \( Y \):
\[
\begin{array}{|c|c|c|c|c|}
\hline
y & 1 & 2 & 3 & 4 \\
\hline
P(Y \leq y) & 0.12 & 0.38 & 0.75 & 1 \\
\hline
\end{array}
\]
(a) What is the probability that a team has two students in Jeffreys’ class?
(b) Compute the probability that a team in Jeffreys’ class has at least 2 students. Compared to Fisher’s from question 2, which class has a higher probability of having teams of at least two students?
(c) Compute the expected team size in Jeffreys’ class. Is it greater than the expected team size in Fisher’s class?
(d) Suppose that in the table of the cdf of \( Y \) the value of \( P(Y \leq 3) \) was missing, that is, suppose you saw the following table:
\[
\begin{array}{|c|c|c|c|c|}
\hline
y & 1 & 2 & 3 & 4 \\
\hline
P(Y \leq y) & 0.12 & 0.38 & ? & 1 \\
\hline
\end{array}
\]
Would it be possible to retrieve \( P(Y \leq 3) \) by using the information available in the table? If yes, show how to do it, if not, briefly explain why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f7b339a-5be8-4a61-96ee-9694aa84ae28%2F12cb1524-2cfe-4dd1-9a9d-126c0f3c123d%2F8e9h5gbf_processed.png&w=3840&q=75)
Transcribed Image Text:3. Sir Harold Jeffreys, doesn’t like the way Fisher teaches statistics and decides to teach a class on ‘Bayesian Statistics’. Toward the end of the quarter, he also asks his students to form teams of 1 to 4 individuals to work on a group project. Let \( Y \) be the team size for a specific group project in Jeffreys’ class. The following table shows the cdf of \( Y \):
\[
\begin{array}{|c|c|c|c|c|}
\hline
y & 1 & 2 & 3 & 4 \\
\hline
P(Y \leq y) & 0.12 & 0.38 & 0.75 & 1 \\
\hline
\end{array}
\]
(a) What is the probability that a team has two students in Jeffreys’ class?
(b) Compute the probability that a team in Jeffreys’ class has at least 2 students. Compared to Fisher’s from question 2, which class has a higher probability of having teams of at least two students?
(c) Compute the expected team size in Jeffreys’ class. Is it greater than the expected team size in Fisher’s class?
(d) Suppose that in the table of the cdf of \( Y \) the value of \( P(Y \leq 3) \) was missing, that is, suppose you saw the following table:
\[
\begin{array}{|c|c|c|c|c|}
\hline
y & 1 & 2 & 3 & 4 \\
\hline
P(Y \leq y) & 0.12 & 0.38 & ? & 1 \\
\hline
\end{array}
\]
Would it be possible to retrieve \( P(Y \leq 3) \) by using the information available in the table? If yes, show how to do it, if not, briefly explain why.
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