Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] Which of them has a σ of 9 using the probability model approach. a) [12.5968, 2, -2 and -12.5968] B) [12.5968, 4, -2 and -12.5968]

Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] Which of them has a σ of 9 using the probability model approach. a) [12.5968, 2, -2 and -12.5968] B) [12.5968, 4, -2 and -12.5968]

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.5: Simulating Games Of Chance

Problem 37P: The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three...

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In this version of dice blackjack, you toss a single die repeatedly and add up the sum of your dice tosses. Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the house then tosses the die repeatedly. The house stops as soon as its total is 4 or more. If the house totals 8 or more, you win. Otherwise, the higher total wins. If there is a tie, the house wins. Consider the following strategies: Keep tossing until your total is 3 or more. Keep tossing until your total is 4 or more. Keep tossing until your total is 5 or more. Keep tossing until your total is 6 or more. Keep tossing until your total is 7 or more. For example, suppose you keep tossing until your total is 4 or more. Here are some examples of how the game might go: You toss a 2 and then a 3 and stop for total of 5. The house tosses a 3 and then a 2. You lose because a tie goes to the house. You toss a 3 and then a 6. You lose. You toss a 6 and stop. The house tosses a 3 and then a 2. You win. You toss a 3 and then a 4 for total of 7. The house tosses a 3 and then a 5. You win. Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values so that you are 95% sure that your probability of winning is between these two values? Which of the five strategies appears to be best?
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
Suppose that you have two four-sided dice that are each equally weighted (i.e. equal chance of any of the four sides landing face up). One of them has values [12.5968, 2, -2 and -12.5968] , the other [12.5968, 4, -2 and -12.5968] . Which of them has a µ of zero using the probability model approach. 1. [12.5968, 4, -2 and -12.5968] 2. [12.5968, 2, -2 and -12.5968]
7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran- dom variable with cumulative distribution function F(t) = 1 – e/10 – (1/10) e¯/10 for all t> 0. a. What is the probability density function of T? b. What is the probability that a piece of equipment survives more than 20 years? c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years? d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years? 8. For the equipment mentioned in Problem 7, a. Derive the failure rate function r(1), and draw a graph of the function. b. Without using the failure rate function, determine the probability that a piece of equipment that has survived 20 years of operation fails in the 21st year. c. Does r(20) accurately estimate your answer to part (b)? Why or why not?
Which of the following is a likely source of basis risk? All of these None of these Crude oil is being used to hedge the price risk of downstream (refined) petroleum product O The termination date of exposure is two weeks later than the contract expiration date. A power plant in the Northeast is managing its input (natural gas) risk using a contract priced at Henry Hub, Louisiana.
|At the Pleasant Haven Hotel there are 36 rooms. The profit earned when a room is sold for a night is $53. If Pleasant Haven overbooks, by selling more reservaitions than they have rooms and they end up having a customer whose reservation cannot be fulfilled, the loss to Pleasant Haven is $30 for that customer. Regardless of the number of rooms booked, the probability of one no show is 60% and the probability of 2 no shows is 20%. There is zero probability of more than 2 no shows. For a night when requests are exceeding the 36 rooms, what is the optimal number of reservations to accept? Assume there is no penalty for a customer who does not show up, i.e., Pleasant Haven does not make $53 on a customer that is a no show. What is the expected net for booking each of the following: (Net means profit minus any overbooking loss.) 36 customers 37 customers 38 customers What is the best number of book?
Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, 0, 4, 5, and 6. Value x of X P (X = x) -3 0 0.23 5 0.17 6 0.30
Planetary Communications, Inc., intends to launch a satellite that will enhance reception of television programs in Alaska. According to its designers, the satellite will have an expected life of sixyears. Assume the exponential distribution applies. Determine the probability that it will functionfor each of the following time periods:a. More than 9 years
A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and twohave a probability of .99. What is the overall probability that the product will function properly?
Planetary Communications, Inc., intends to launch a satellite that will enhance reception of television programs in Alaska. According to its designers, the satellite will have an expected life of sixyears. Assume the exponential distribution applies. Determine the probability that it will functionfor each of the following time periods: b. Less than 12 years
If events X and Y are mutually exclusive then A- P(X)P(Y) = 0 B- they are independent events C- their joint probability is zero D- P(X)P(Y) = P(X | Y)