Suppose that a basketball player’s success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?

Suppose that a basketball player’s success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?

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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Appointments in a medical office are scheduled every 15 minutes. Throughout the day, appointments will be running on time or late, depending on the previous appointment only, according to the following matrix of transition probabilities: Previous Appointment Next Appointment On Time Late On Time .70 .30 Late .45 .55 What are the steady state probabilities?
The management is faced with the problem of choosing one of the products for manufacturing. The probability matrix after market research for the two products was as follows: State of nature Acts Good Fair Рoor Product 'A' 0.75 0.15 0.10 Product 'B' 0.60 0.30 0.10 The profits that the management can make for different levels of market acceptability of the products are as follows : Profit (in USD) if market is Acts Good Fair Рoor Product 'A' 35,000 15,000 5,000 Product 'B' -1,000 20,000 Loss 3,000 Calculate expected value of the choice of alternative and advise the management.
5. Markov's Chains Once a year employees at a company are given the opportunity to join one of three pension plans, A, B, or C. Once an employee decides to join one of these plans, the employee cannot drop the plan or switch to another plan. Past records indicate that each year 4% of the employees elect to join plan A, 14% elect to join plan B, 7% elect to join plan C, and the remainder do not join any plan. (A) In the long run, what percentage of the employees will elect to join plan A? Plan B? Plan C? (B) On the average, how many years will it take an employee to decide to join a plan?
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The Tiger Sports Shop1 has hired you as an analyst to understand its market position with respect to Clemson merchandise. It is particularly concerned about its major competitor, Mr. Knickerbocker, and which Clemson-related store has the ‘lead’ market share. Recent history has suggested that which Clemson-related store has the ‘lead market share’ can be modeled as a Markov Chain using three states: TSS (Tiger Sports Shop), MK (Mr. Knickerbocker), and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data in the picture. a) The current state of the lead market share in October is that Tiger Sports Shop is in the lead (i.e., the Markov Chain in October is TSS). Tiger Sports Shop is considering launching a new brand in February only if it has the lead market share in January. Determine the probability that TSS will launch this new brand. Please show any equations or matrices…
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