Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 2.2, Problem 10E
In the casino game called high—low, there are three possible bets. Assume that $1 is the size of the bet. Two fair six-sided dice are rolled and their sum is calculated. If you bet low, you win $1 if the sum of the dice is (2,3,4,5,6). If you bet high, you win $1 if the sum of the dice is (8,9, 10, 11, 12). If you bet on (7), you win $4 if a sum of 7 is rolled. Otherwise, you lose on each of the three bets. In all three cases, your original dollar is returned if you win. Find the
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Suppose you decided to play a gambling game. In order to play the game there is a $1.50 dollar fee to play. If you roll a 1, 2, or 3 you win nothing (i.e., your net profit is $-1.50). If you roll a 4 or 5, you win $3.50 (i.e., your net profit is $2.00). If you roll a 6 you win $5.00 (i.e., your net profit is $3.50).Use the information described above to construct a probability distribution table for the random variable xx which represents the net profit of your winnings. Note: Be sure to enter your probabilities as reduced fractions.
Die Roll
xx
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Roll a 4 or 5
Roll a 6
Find the amount you would expect to win or lose each time you played the game. Round your final answer to two decimal places.μ=
Chapter 2 Solutions
Probability and Statistical Inference (9th Edition)
Ch. 2.1 - Let the pmf of X be defined by f(x)=x9,x=2,3,4.....Ch. 2.1 - Let a chip be taken at random from a bowl that...Ch. 2.1 - For each of the following, determine the constant...Ch. 2.1 - The state of Michigan generates a three-digit...Ch. 2.1 - The pmf of X is f(x)=(5x)10,x=1,2,3,4. (a) Graph...Ch. 2.1 - Let a random experiment consist of rolling a pair...Ch. 2.1 - Let a random experiment be the casting of a pair...Ch. 2.1 - A fair four-sided die has two faces numbered 0 and...Ch. 2.1 - Let the pmf of X be defined by...Ch. 2.1 - Prob. 10E
Ch. 2.1 - In a lot (collection) of 100 light bulbs, there...Ch. 2.1 - Let X be the number of accidents per week in a...Ch. 2.1 - A professor gave her students six essay questions...Ch. 2.1 - Often in buying a product at a supermarket, there...Ch. 2.1 - Five cards are selected at random without...Ch. 2.1 - Prob. 16ECh. 2.1 - A bag contains 144 ping-pong balls. More than half...Ch. 2.2 - Find E(X) for each of the distributions given in...Ch. 2.2 - Let the random variable X have the pmf...Ch. 2.2 - Let X be a discrete random variable with the...Ch. 2.2 - Prob. 4ECh. 2.2 - Let the random variable X be the number of days...Ch. 2.2 - Let the pmf of X be defined by...Ch. 2.2 - In Example 2.2-1 let Z=u(X)=X3. (a) Find the pmf...Ch. 2.2 - Let X be a random variable with support...Ch. 2.2 - In the gambling game chuck-a-luck, for a $1 bet it...Ch. 2.2 - In the casino game called high—low, there are...Ch. 2.2 - A roulette wheel used in an American casino has 38...Ch. 2.2 - Suppose that a school has 20 classes: 16 with 25...Ch. 2.3 - Find the mean, variance, and index of skewness for...Ch. 2.3 - For each of the following distributions, find...Ch. 2.3 - If the pmf of X is given by f(x), (I) depict the...Ch. 2.3 - Let and 2 denote the mean and variance of the...Ch. 2.3 - Consider an experiment that consists of selecting...Ch. 2.3 - Place eight chips in a bowl: Three have the number...Ch. 2.3 - Let X equal an integer selected at random from the...Ch. 2.3 - Let X equal the larger outcome when two fair...Ch. 2.3 - A warranty is written on a product worth $10,000...Ch. 2.3 - Let X be a discrete random variable with pmf...Ch. 2.3 - If the moment-generating function of X is...Ch. 2.3 - Let X equal the number of people selected at...Ch. 2.3 - For each question on a multiple-choice test, there...Ch. 2.3 - The probability that a machine produces a...Ch. 2.3 - Apples are packaged automatically in 3-pound bags....Ch. 2.3 - Let X equal the number of flips of a fair coin...Ch. 2.3 - Let X equal the number of flips of a fair coin...Ch. 2.3 - Let X have a geometric distribution. Show that...Ch. 2.3 - Given a random permutation of the integers in the...Ch. 2.4 - An urn contains seven red and 11 white balls. Draw...Ch. 2.4 - Suppose that in Exercise 2.4-1, X = 1 if a red...Ch. 2.4 - On a six-question multiple-choice test there are...Ch. 2.4 - It is claimed that 15% of the ducks in a...Ch. 2.4 - In a lab experiment involving inorganic syntheses...Ch. 2.4 - It is believed that approximately 75% of American...Ch. 2.4 - Suppose that 2000 points are selected...Ch. 2.4 - A boiler has four relief valves. The probability...Ch. 2.4 - Suppose that the percentage of American drivers...Ch. 2.4 - A certain type of mint has a label weight of 20.4...Ch. 2.4 - Find the index of skewness for the b(n,p)...Ch. 2.4 - In the casino game chuck-a-luck, three fair six-...Ch. 2.4 - It is claimed that for a particular lottery, 110...Ch. 2.4 - For the lottery described in Exercise 2.4-13, find...Ch. 2.4 - A hospital obtains 40% of its flu vaccine from...Ch. 2.4 - A company starts a fund of M dollars from which it...Ch. 2.4 - Your stockbroker is free to take your calls about...Ch. 2.4 - In group testing for a certain disease, a blood...Ch. 2.4 - Define the pmf and give the values of ,2, and ...Ch. 2.4 - Prob. 20ECh. 2.5 - An excellent free-throw shooter attempts several...Ch. 2.5 - Show that 63512 is the probability that the fifth...Ch. 2.5 - Suppose that a basketball player different from...Ch. 2.5 - Suppose an airport metal detector catches a person...Ch. 2.5 - Let the moment-generating function M(t) of X exist...Ch. 2.5 - Use the result of Exercise 2.6-5 to find the mean...Ch. 2.5 - If E(Xr)=5r,r=1,2,3.... find the moment-generating...Ch. 2.5 - The probability that a companys workforce has no...Ch. 2.5 - One of four different prizes was randomly put into...Ch. 2.5 - In 2016, Red Rose tea randomly began placing one...Ch. 2.6 - Let X have a Poisson distribution with a mean of...Ch. 2.6 - Let X have a Poisson distribution with a variance...Ch. 2.6 - Customers arrive at a travel agency at a mean rate...Ch. 2.6 - If X has a Poisson distribution such that...Ch. 2.6 - Flaws in a certain type of drapery material appear...Ch. 2.6 - Find the index of skewness of a Poisson...Ch. 2.6 - With probability 0.001, a prize of $499 is won in...Ch. 2.6 - Suppose that the probability of suffering a side...Ch. 2.6 - A store selling newspapers orders only n = 4 of a...Ch. 2.6 - The mean of a Poisson random variable X is =9....Ch. 2.6 - An airline always overbooks if possible. A...Ch. 2.6 - A baseball team loses $100,000 for each...Ch. 2.6 - Assume that a policyholder is four times more...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- You toss two six-sided dice. What is the probability that the total of the two dice is 5?arrow_forwardIn American roulette, the wheel contains the numbers 1 through 36 alternating between black and red. There are two green spaces numbered 0 and 00. A player places a bet of $4.25 on red to play the game. If the ball lands on red, the player gets a $4.25 for winning and receives the money back. If the ball does not land on red, then the player simply loses the $4.25 placed on the bet. Calculate the expected winnings on one game. Round your answer to the nearest cent.arrow_forwardat a casino, you throw a fair 4 sided dice whose sides are labeled 1, 2, 3 and 4. If you land on a one, you get thirty dollars. If you land on a two, you get ten dollars. If you land on either a three or four, you owe the casino eight dollars. If you repeatedly play this game, what would your "winnings" be on average, in dollars?arrow_forward
- Suppose you decided to play a gambling game. In order to play the game there is a $1.00 dollar fee to play. If you roll a 1, 2, or 3 you win nothing (i.e., your net profit is $-1.00). If you roll a 4 or 5, you win $2.50 (i.e., your net profit is $1.50). If you roll a 6 you win $4.00 (i.e., your net profit is $3.00).Use the information described above to construct a probability distribution table for the random variable xx which represents the net profit of your winnings. Note: Be sure to enter your probabilities as reduced fractions. Die Roll xx P(x)P(x) Roll a 1, 2, or 3 Roll a 4 or 5 Roll a 6 Find the amount you would expect to win or lose each time you played the game. Round your final answer to two decimal places.μ=arrow_forwardHadey is running a game of chance to raise money for a trip to Jamaica to visit his grandparents. A player pays $5 and then rolls a six-sided die. The faces of the die are different colors, one red, one blue, one yellow, one green, one purple and one orange. If the die comes up green, Hadey pays the player $20. Old Billie plays the game 120 times and loses $300. She doesn't trust Hadey and asks Letecia to test the die that Hadey is using for bias. Letecia rolls the die 600 times with the following results. yellow Red blue green 73 purple Orange 99 107 104 108 109 Perform the appropriate hypothesis test at the 0.05 significance level to determine if the die is balanced.arrow_forwardYou play a game where you roll two dice. It was decided that you lose ₱500 if you get a sum of 3, 6, or 9, and you lose ₱400 if you get a sum of 10. However, you win ₱300 for anything else. If you continue to play the game, how much do you expect to win or lose in the game in the long run?arrow_forward
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