A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 8, Problem 8.8TE
Explain why a gamma random variable with parameters
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The Martinezes are planning to refinance their home. The outstanding balance on their original loan is $150,000. Their finance company has offered them two options. (Assume there are no additional finance charges. Round your answers to the nearest cent.)
Option A: A fixed-rate mortgage at an interest rate of 4.5%/year compounded monthly, payable over a 30-year period in 360 equal monthly installments.Option B: A fixed-rate mortgage at an interest rate of 4.25%/year compounded monthly, payable over a 12-year period in 144 equal monthly installments.
(a) Find the monthly payment required to amortize each of these loans over the life of the loan.
option A $
option B $
(b) How much interest would the Martinezes save if they chose the 12-year mortgage instead of the 30-year mortgage?
The Martinezes are planning to refinance their home. The outstanding balance on their original loan is $150,000. Their finance company has offered them two options. (Assume there are no additional finance charges. Round your answers to the nearest cent.)
Option A: A fixed-rate mortgage at an interest rate of 4.5%/year compounded monthly, payable over a 30-year period in 360 equal monthly installments.Option B: A fixed-rate mortgage at an interest rate of 4.25%/year compounded monthly, payable over a 12-year period in 144 equal monthly installments.
(a) Find the monthly payment required to amortize each of these loans over the life of the loan.
option A $
option B $
(b) How much interest would the Martinezes save if they chose the 12-year mortgage instead of the 30-year mortgage?
When a tennis player serves, he gets two chances to serve in bounds. If he fails to do so twice, he loses the point. If he
attempts to serve an ace, he serves in bounds with probability 3/8.If he serves a lob, he serves in bounds with probability
7/8. If he serves an ace in bounds, he wins the point with probability 2/3. With an in-bounds lob, he wins the point with
probability 1/3. If the cost is '+1' for each point lost and '-1' for each point won, the problem is to determine the optimal
serving strategy to minimize the (long-run)expected average cost per point. (Hint: Let state 0 denote point over,two
serves to go on next point; and let state 1 denote one serve left.
(1). Formulate this problem as a Markov decision process by identifying the states and decisions and then finding the
Cik.
(2). Draw the corresponding state action diagram.
(3). List all possible (stationary deterministic) policies.
(4). For each policy, find the transition matrix and write an expression for the…
Chapter 8 Solutions
A First Course in Probability
Ch. 8 - Suppose that X is a random variable with mean and...Ch. 8 - From past experience, a professor knows that the...Ch. 8 - Use the central limit theorem to solve part (c) of...Ch. 8 - Let X1,...,X20 be independent Poisson random...Ch. 8 - Fifty numbers are rounded off to the nearest...Ch. 8 - A die is continually rolled until the total sum of...Ch. 8 - A person has 100 light bulbs whose lifetimes are...Ch. 8 - In Problem 8.7, suppose that it takes a random...Ch. 8 - If X is a gamma random variable with parameters...Ch. 8 - Civil engineers believe that W, the amount of...
Ch. 8 - Many people believe that the daily change of price...Ch. 8 - We have 100 components that we will put in use in...Ch. 8 - Student scores on exams given by a certain...Ch. 8 - A certain component is critical to the operation...Ch. 8 - An insurance company has 10.000 automobile...Ch. 8 - A.J. has 20 jobs that she must do in sequence,...Ch. 8 - Redo Example 5b under the assumption that the...Ch. 8 - Repeat part (a) of Problem 8.2 when it is known...Ch. 8 - A lake contains 4 distinct types of fish. Suppose...Ch. 8 - If X is a nonne9ative random variable with mean...Ch. 8 - Let X be a nonnegative random variable. Prove that...Ch. 8 - Prob. 8.22PCh. 8 - Let X be a Poisson random variable with mean 20....Ch. 8 - Prob. 8.24PCh. 8 - If X has variance 2, then , the positive square...Ch. 8 - If X has mean and standard deviation , the ratio...Ch. 8 - Compute the measurement signal-to-noise ratio-that...Ch. 8 - Let Zn,n1, be a sequence of random variables and...Ch. 8 - Prob. 8.5TECh. 8 - Prob. 8.6TECh. 8 - Prob. 8.7TECh. 8 - Explain why a gamma random variable with...Ch. 8 - Prob. 8.9TECh. 8 - If X is a Poisson random variable with mean , show...Ch. 8 - Prob. 8.11TECh. 8 - Prob. 8.12TECh. 8 - Prob. 8.13TECh. 8 - Prob. 8.14TECh. 8 - The number of automobiles sold weekly at a certain...Ch. 8 - Prob. 8.2STPECh. 8 - If E[X]=75E[Y]=75Var(X)=10var(Y)=12cov(X,Y)=3 give...Ch. 8 - Prob. 8.4STPECh. 8 - Prob. 8.5STPECh. 8 - Prob. 8.6STPECh. 8 - Prob. 8.7STPECh. 8 - Prob. 8.8STPECh. 8 - Prob. 8.9STPECh. 8 - A tobacco company claims that the amount of...Ch. 8 - Prob. 8.11STPECh. 8 - Prob. 8.12STPECh. 8 - The strong law of large numbers states that with...Ch. 8 - Each new book donated to a library must be...
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