To determine Find the average loss of a gambler in dollars. Explanation Answers may vary; one of the possible answers is given below: It is given that, bookmakers include the concept of point spread while taking bets on sports team. Point spread gives extra points to weaker them by making the outcome of the bet to a tossup. A gambler bets $10 and picks the winners of five games. If the gambler wins in less than 3 games, then he loses $10, the gambler gets $10 if he wins in 3 games, gets $20 if he wins in 4 games, gets $50 if he wins in 5 games. Simulation: A simulation is imitating the reality by using random numbers to represent the outcomes of real events Steps for simulating a component: Identify the component to be repeated. Explain how to model the components outcome. Components : A characteristic of the individuals in the population, which an investigator is interested to study, is called a component. Here, the investigator wants to estimate the average amount given away by the gambler. The gamblers expected winnings gives the average loss of the gambler. Hence, it is needed to find the expected winnings of gambler. One game is a component, but the components outcome is not the objective of the study. The sequence of the components has to be observed to analyze the study. Thus, one game is a component of the study to run the simulation. Here, it is given that, the gambler loses $10 if he wins in less than 3 games, gains $10 if he wins in 3 games, gains $20 if he wins in 4 games and gains $50 if he wins in 5 games. Here, the investigator introduced the concept of “point spread”. In theory point spread indicates that the outcome of the bet is a tossup. That is, there is equal chance of winning and losing the game. Hence, the probability for a loss and win in a game is equal. Simulating a component: Step-1: Generate one digit random numbers 0-9. Let the digits 0-4 represents a loss. Let the digits 5-9 represents a win. Since, the bet consists of five games, generate five digits at a time. The gambler loses $10 if he wins in less than 3 games. That is, the gambler loses $10, if the trail consists of 0, 1 or 2 numbers in between 5-9. The gambler gains $10 if he wins in 3 games. That is, the gambler gains $10, if the trail consists of 3 numbers in between 5-9. The gambler gains $20 if he wins in 4 games. That is, the gambler gains $20, if the trail consists of 4 numbers in between 5-9. The gambler gains $50 if he wins in 5 games. That is, the gambler gains $50, if all the 5 numbers in the trail fall in between 5-9. Combining the components to model a trail: Let us have the simulation for 5 trails. Simulating a trail: Generate the random numbers for 5 times. Note the amount gained or the loss of gambler in each trail. Random data : Software procedure: Step by step procedure to obtain the random data using the MINITAB software: Choose Calc > Random data > Sample from columns. In Number of rows to sample enter 5. In From columns, enter the column input which consists of 0 to 9 numbers...

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Author: DeVeaux

Publisher: PEARSON

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Chapter R, Problem 3.19RE

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