Draw the transition probability graph and construct the transition probability matrix of thefollowing problems.3. (Cyert and Associates, 1963) Bank1 offers loans which are either paid when due or are delayed. If thepayment on a loan is delayed more than 4 quarters (1 year), Bank con siders the loan a bad debt and writesit off. The following table provides a sample of Bankl's past experience with loansLoan amount Quarters late Payment history$2000 paid, $3000 delayed by an extra quarter, $3000 delayed by 2extra quarters, and the rest delayed 3 extra quarters.$4000 paid, $12,000 delayed by an extra quarter, $6000 delayed by2 extra quarters, and the rest delayed by 3 extra quarters.$7500 paid, $15,000 delayed by an extra quarter, and the restdelayed by 2 extra quarters.$42,000 paid and the rest delayed by an extra quarter.$50,000 paid.$10,000$25,0001$50,00023.SS0,000$100,0004

We have to construct probability transitions matrix

Answered: Draw the transition probability graph…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question 4A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. Part AAnswer the following questions:a. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service ( Lq)?c. What is the average number of customers in the system (L)?d. What is the average time a customer waits for service(Wq)?e. What is the average time in the system (W)?f. What is the probability that a customer will have to wait for service (Pw)?g…
“Passive investors outperform active investors during recession”. Discuss the statement citingexamples.A stockbroker calls you and suggests that you invest in the Ambrick Company. After analyzingthe firm’s annual report and other material, you believe that the distribution of rates of return is asfollows: Possible Rate of Return Probability -0.60 0.05 -0.3 0.20 -0.10 0.10 0.20 0.30 0.40 0.20 0.80 0.15 Compute the expected return [E(Ri)] on Ambrick stock
Which of the following are reasons why a process would be considered stochastic? 1. we lack of data on the variable of interest/generating process 2. we lack quantitative understanding of the generating process 3. the generating process itself is random 4. the process can be modelled with certainty 5. the generating process changes over time
1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Question 5: A department store prints scratch-and-save discount coupons to distribute to its customers. The numbers for each present discount are shown in the table. Present Discount Number of Each type of discount Available 60% 50 50% 25000 30% 50000 10% 500,000 Determine the expected percent discount. Question 6: An examination consists of 50 multiple-choice items, each with 4 possible answers. what is the probability of guessing 25 or more correct answers? Question 7: A. bank found that 25% of its loans to new small business become delinquent. Ten small business are selected randomly from the bank's files. a) what is probability that three of them are delinquent? b) what is the probability that at least three of them are delinquent? c) what is the expected delinquency? B. Geometric Distribution Q8: Explain why rolling a die until 3 shows can be modelled by a geometric distribution
To maximize the probability that customers purchase products during a visit to a website, a company that provides marketing services and website management experiments with different offers and website design to understand customer Web behavior. Possible actions by the website include offering the customer an instant discount, offering the customer free shipping, or doing nothing. A recent experiment found that customers make purchases 6% of the time when offered the instant discount, 4% when offered free shipping, and 3% when no special offer was given. Suppose 30% of the customers are offered the discount and an additional 40% are offered free shipping. Complete parts a through c. a) Construct a probability tree for this experiment. Complete the probability tree below. Discount .30 -Free Shipping .40 Nothing - Purchase No Purchase Purchase No Purchase Purchase No Purchase (Type integers or decimals.) 0.6 -Discount and Purchase 0.94 Discount and No Purchase - Shipping and Purchase -…
*Question Six* The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £2. What is the probability that the expenditure of the first customer exceeds the expenditure of the second customer by at least 20 £?
Q. 1 Suppose that 4.5% of all adults over 50 have cancer. A certain physician correctly diagnoses 94% of all adults over 50 with cancer as having the disease and incorrectly diagnoses 4% of all adults over 50 without cancer as having the disease. (i) Draw a tree diagram and label it with appropriate probabilities. (ii) Find the probability that a randomly-selected adult over 50 is diagnosed as not having cancer. (iii) Find the probability that a randomly-selected adult over 50 actually has cancer, given that he/she is diagnosed as not having cancer.
Question C

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