A script that will prompt the user for a character and then create an x- vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

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Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

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Suppose that the number of expensive goods X sold in a shop over 24 days, is Poisson random variable with rate 240, i.e. X Poisson (240), where > 0 is the expected number of sales per day and is the unknown parameter that we would like to estimate. Suppose further that can take three possible values 0₁ = 1/2, 0, 1/4 and 0₁ = 1/8, with prior probabilities 0.2, 0.5 and 0.3, respectively. Suppose now that we observe that x=10 expensive goods were sold in the last 24 days. (a) Write down the likelihood function for and find the MLE of 0. (b) Given the observed data 2 = 10, what is the posterior distribution of 0, p(0 | x= 10)? (c) What is the posterior mean for ? (d) What is the posterior standard deviation for 0? [Hint: You may use the fact if X is a random variable, then var(X) = E(X²) – [E(X)]²].

A machine is built to make mass-produced items. Each item made by the machine has a probability of being defective. Given the value of 0, the items are independent of each other, where is unknown and would like to estimate. Suppose has for prior distribution a Beta(a, ß) distribution, where a > 0 and 3>0. The machine is tested by producing items until the first defective occurs. Suppose that the first 12 items are not defective but the y = 13th item is defective. (a) Write down the likelihood function for 0 and find the MLE of 0. (b) Given the observed data y = 13, what is the posterior distribution of 0, p(0 | y = 13)? Take a = 1 and ẞ= 19. (c) What are the parameters of the posterior distribution? (d) What is the posterior mean for 0? (e) What is the posterior standard deviation? =

Suppose that the number of expensive goods X sold in a shop over 24 days, is Poisson random variable with rate 240, i.e. X Poisson (240), where > 0 is the expected number of sales per day and is the unknown parameter that we would like to estimate. Suppose further that can take three possible values 0₁ = 1/2, 0, 1/4 and 0₁ = 1/8, with prior probabilities 0.2, 0.5 and 0.3, respectively. Suppose now that we observe that x=10 expensive goods were sold in the last 24 days. (a) Write down the likelihood function for and find the MLE of 0. (b) Given the observed data 2 = 10, what is the posterior distribution of 0, p(0 | x= 10)? (c) What is the posterior mean for ? (d) What is the posterior standard deviation for 0? [Hint: You may use the fact if X is a random variable, then var(X) = E(X²) – [E(X)]²].

Answer 2

Question

Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

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Answer 3

Question

Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

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Answer 4

Question

Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

Expert Solution & Answer

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Answer 5

Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

Answer 6

Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

Answer 7

Chapter 4, Problem 10E

To determine

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

Ch. 4 - Prob. 4.1P Ch. 4 - Prob. 4.2P Ch. 4 - Prob. 4.3P Ch. 4 - Prob. 4.4P Ch. 4 - Prob. 4.5P Ch. 4 - Prob. 1E Ch. 4 - Prob. 2E Ch. 4 - Prob. 3E Ch. 4 - Prob. 4E Ch. 4 - Prob. 5E

A script that will prompt the user for a character and then create an x- vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

Solution Summary: The author explains how to create an x-vector with 50 numbers, equally spaced between 2 and 2, and then a cos(x). If the character color is red, the graph is plot

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To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

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Chapter 4 Solutions

A script that will prompt the user for a character and then create an x- vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

Solution Summary: The author explains how to create an x-vector with 50 numbers, equally spaced between 2 and 2, and then a cos(x). If the character color is red, the graph is plot

Concept explainers

Videos

To write: A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).

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Chapter 4 Solutions

To write:

A script that will prompt the user for a character and then create an x-vector that has 50 numbers, equally spaced between −2π and 2π, and then a y-vector which is cos(x).