![Problem 4 ((30 points) Bayes Theorem). The local barber shop is home to three barbers The barbers appear identical but vary in their ability to provide good haircuts. Denote the event that you receive a good haircut by G, the event that you do not receive a good haircut by NG, and the event that your hair is cut by barber i by Bi, where i E 1,2, 3) The probability that any particular barber cuts your hair is 1/3. The probability that you receive a good haircut from barber 1 is 1. The probability that you receive a good haircut from barber 2 is 1/2. The probability that you receive a good haircut from barber 3 is x, where z E [0,1] Recall: Let Ai, A2,..., Ak are disjoint and exhaustive events in the sample space S, such that P(A) > 0, let B be an event such that P(B) > 0. Then, P(B) P(BA)P(A) (Law of Total Probability) A,|3)-PBA (Bayes Theorem) a. Using the Bayes Theorem calculate the probability that your hair is cut by barber 1 given that you received a good haircut b. Assume P(G)- Find z.](http://img.homeworklib.com/questions/ea5e46e0-225f-11ec-8531-3b4c8b46d00b.png?x-oss-process=image/resize,w_560)
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Problem 4 ((30 points) Bayes Theorem). The local barber shop is home to three barbers The...
17.2-2.* Newell and Jeff are the two barbers in a barber shop they own and operate....
17.2-2.* Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs for customers who are waiting to begin a haircut, so the number of customers in the shop varies between 0 and 4. For n 0. 1. 2. 3. 4, the probability P that exactly n customers are in the shop is P0= P, = (a) Calculate L. How would you describe the meaning of L to Newell and Jeff? (b)...
Vin Diesel owns the Blue Spruce Barber Shop. He employs 5 barbers and pays each a...
Vin Diesel owns the Blue Spruce Barber Shop. He employs 5
barbers and pays each a base rate of $1,490 per month. One of the
barbers serves as the manager and receives an extra $550 per month.
In addition to the base rate, each barber also receives a
commission of $4.50 per haircut.
Other costs are as follows.
Advertising
$270
per month
Rent
$990
per month
Barber supplies
$0.30
per haircut
Utilities
$185
per month plus $0.20 per haircut
Magazines...
Problem 11-1 (Part Level Submission) Vin Diesel owns the Blue Spruce Barber Shop. He employs 5...
Problem 11-1 (Part Level Submission)
Vin Diesel owns the Blue Spruce Barber Shop. He employs 5 barbers
and pays each a base rate of $1,490 per month. One of the barbers
serves as the manager and receives an extra $550 per month. In
addition to the base rate, each barber also receives a commission
of $4.50 per haircut.
Other costs are as follows.
Advertising
$270
per month
Rent
$990
per month
Barber supplies
$0.30
per haircut
Utilities
$185
per month...
according to bayes theorem , the probability of event a , given that event b has occured is as follows p(a)=1/4. p(a')=...
according to bayes theorem , the probability of event a , given that event b has occured is as follows p(a)=1/4. p(a')=3/4, p(b/a)=1/7, and p(b/a')=7/10 The probability of event a , given that event b has occurred is p(a/b)=
e. Application of Bayes: Using Bayes theorem driven in item d, show that in the following problem switching is the bett...
e. Application of Bayes: Using Bayes theorem driven in item d, show that in the following problem switching is the better strategy for the player and makes the probability of wining as 2/3, while not switching gives the probability of wining 1/3. Monty Hall: There are 3 doors 1, 2, 3. Randomly, and equally likely, behind one of the door there is a prize, and other two are empty. The player choose one door. He does not open the door...
1. Which of the following is an implication of Bayes' Theorem? A. It is irrational to...
1. Which of the following is an implication of Bayes' Theorem? A. It is irrational to believe in extraordinary claims B. Extraordinar C. Extraordinary claims cannot D. No evidence can be trusted E. We should treat all claims as equally likely, until we see the data at han<d y claims require extraordinary evidence be true 2. According to Slovic et al., which of the following causes of death tend to be overestimated? A. Stomach Cancer B. Lightning C. Tornadoes D....
This question is about the Bayes' Theorem. You are given two boxes. Box 1 contains 5...
This question is about the Bayes' Theorem. You are given two boxes. Box 1 contains 5 red, 5 green, and 3 blue balls, and Box 2 contains 4 red, 3 green, and 2 yellow balls. You are asked to randomly pick one of the two boxes. Holding that box, you grab one ball at random, and then set the box back down. You found out that it is a red ball. Let A be the event that you choose Box...
13. (Bayes' Theorem). Company makes product at three factories. From past records, they know the proportion...
13. (Bayes' Theorem). Company makes product at three factories. From past records, they know the proportion of output from each factory and the percentage of defects that come from each factory. The information is shown in the table. Defects (%) L Output (%) 20 15 65 A quality control engineer selects a ski binding at random. Let B1, B2, and Bs represent the event that the binding comes from factory 1, factory 2, or factory 3, respectively, and let A...
Problem 1.4 You are lost in the basement of the Photonics center where the population is...
Problem 1.4 You are lost in the basement of the Photonics center where the population is entirely composed of students and professors. You are looking for the exit, which you've decided is equally likely to be to the East or to the West. The students comprise two-thirds of the population, and any one student gives a correct answer to a request for directions with probability 3/4. (Assume answers to repeated questions are independent, even if the question and the person...
1. A fair coin is tossed three times. Let A be the event that there are...
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? (5) c. Compute P(A), P(B), P(A|B), and P(BA). [7] 2. Let U be a continuous random variable with...
17.2-2.* Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs for customers who are waiting to begin a haircut, so the number of customers in the shop varies between 0 and 4. For n 0. 1. 2. 3. 4, the probability P that exactly n customers are in the shop is P0= P, = (a) Calculate L. How would you describe the meaning of L to Newell and Jeff? (b)...
Vin Diesel owns the Blue Spruce Barber Shop. He employs 5
barbers and pays each a base rate of $1,490 per month. One of the
barbers serves as the manager and receives an extra $550 per month.
In addition to the base rate, each barber also receives a
commission of $4.50 per haircut.
Other costs are as follows.
Advertising
$270
per month
Rent
$990
per month
Barber supplies
$0.30
per haircut
Utilities
$185
per month plus $0.20 per haircut
Magazines...
Problem 11-1 (Part Level Submission)
Vin Diesel owns the Blue Spruce Barber Shop. He employs 5 barbers
and pays each a base rate of $1,490 per month. One of the barbers
serves as the manager and receives an extra $550 per month. In
addition to the base rate, each barber also receives a commission
of $4.50 per haircut.
Other costs are as follows.
Advertising
$270
per month
Rent
$990
per month
Barber supplies
$0.30
per haircut
Utilities
$185
per month...
e. Application of Bayes: Using Bayes theorem driven in item d, show that in the following problem switching is the better strategy for the player and makes the probability of wining as 2/3, while not switching gives the probability of wining 1/3. Monty Hall: There are 3 doors 1, 2, 3. Randomly, and equally likely, behind one of the door there is a prize, and other two are empty. The player choose one door. He does not open the door...
1. Which of the following is an implication of Bayes' Theorem? A. It is irrational to believe in extraordinary claims B. Extraordinar C. Extraordinary claims cannot D. No evidence can be trusted E. We should treat all claims as equally likely, until we see the data at han<d y claims require extraordinary evidence be true 2. According to Slovic et al., which of the following causes of death tend to be overestimated? A. Stomach Cancer B. Lightning C. Tornadoes D....
13. (Bayes' Theorem). Company makes product at three factories. From past records, they know the proportion of output from each factory and the percentage of defects that come from each factory. The information is shown in the table. Defects (%) L Output (%) 20 15 65 A quality control engineer selects a ski binding at random. Let B1, B2, and Bs represent the event that the binding comes from factory 1, factory 2, or factory 3, respectively, and let A...
Problem 1.4 You are lost in the basement of the Photonics center where the population is entirely composed of students and professors. You are looking for the exit, which you've decided is equally likely to be to the East or to the West. The students comprise two-thirds of the population, and any one student gives a correct answer to a request for directions with probability 3/4. (Assume answers to repeated questions are independent, even if the question and the person...
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? (5) c. Compute P(A), P(B), P(A|B), and P(BA). [7] 2. Let U be a continuous random variable with...
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