Explanation Given Information: Two dice are rolled, and X is the higher number. Formula Used: For the random variable X, P ( X = x ) represents the random variable X with the particular value of x. If the outcomes of an event are equally likely to occur, then the probability of an event E is given by: P ( E ) = n ( E ) n ( S ) Here n ( E ) is the number of favorable outcomes and n ( S ) is the total number of outcomes. If there are n independent trails associated with the binomial variable X, and the probability of success is p, then the expected value of X is given by, μ = x 1 ⋅ P ( X = x 1 ) + x 2 ⋅ P ( X = x 2 ) + ... + x n ⋅ P ( X = x n ) If there are n independent trails associated with the binomial variable X, and the probability of success is p, and the probability of failure is q then the variance is given by, σ 2 = ∑ i = 1 n ( x i − μ ) 2 ⋅ P ( X = x i ) The standard deviation of X is the square root of the variance given by: σ = σ 2 Calculation: Consider the probability distribution for the random variable X . The possible value of the variable X is 1 , 2 , 3 , 4 , 5 , 6 . Total number of outcomes when two die rolled is 36 . The probability that number 1 appears on both die, P ( X = 1 ) is 1 36 . The probability that either 1 or 2 appears on both dies, P ( X = 2 ) = P { ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) } is 3 36 . The probability that numbers from 1 , 2 or 3 appears on both die, P ( X = 3 ) = P { ( 1 , 3 ) , ( 2 , 3 ) , ( 3 , 3 ) , ( 3 , 2 ) , ( 3 , 1 ) } is 5 36 . The probability that numbers from 1 , 2 , 3 or 4 appears on both die, P ( X = 4 ) = P { ( 1 , 4 ) , ( 2 , 4 ) , ( 3 , 4 ) , ( 4 , 4 ) ( 4 , 4 ) , ( 4 , 2 ) , ( 4 , 1 ) } is 7 36 . The probability that numbers from 1 , 2 , 3 , 4 or 5 appears on both die, P ( X = 5 ) = P { ( 1 , 5 ) , ( 2 , 5 ) , ( 3 , 5 ) , ( 4 , 5 ) , ( 5 , 5 ) , ( 5 , 4 ) , ( 5 , 3 ) , ( 5 , 2 ) , ( 5 , 1 ) } is 9 36 . The probability that numbers from 1 , 2 , 3 , 4 , 5 or 6 appears on both die, P ( X = 6 ) = P { ( 1 , 6 ) , ( 2 , 6 ) , ( 3 , 6 ) , ( 4 , 6 ) , ( 5 , 6 ) , ( 6 , 6 ) , ( 6 , 5 ) , ( 6 , 4 ) , ( 6 , 3 ) , ( 6 , 2 ) , ( 6 , 1 ) } is 11 36 The probability distribution of the variable X , where X is the larger of the two numbers facing up is as follows, x 1 2 3 4 5 6 P ( X = x ) 0.0278 0.0833 0.1389 0.1944 0.25 0.3056 Calculate the value of x ⋅ P ( X = x ) for the X = 1 , 1 ⋅ P ( X = 1 ) = 1 ⋅ ( 0.0278 ) = 0.0278 Calculate the value of x ⋅ P ( X = x ) for the X = 2 , 2 ⋅ P ( X = 2 ) = 2 ⋅ ( 0.0833 ) = 0.1667 Calculate the value of x ⋅ P ( X = x ) for the X = 3 , 3 ⋅ P ( X = 3 ) = 3 ⋅ ( 0.1389 ) = 0.4167 Calculate the value of x ⋅ P ( X = x ) for the X = 4 , 4 ⋅ P ( X = 4 ) = 4 ⋅ ( 0.1944 ) = 0.7776 Calculate the value of x ⋅ P ( X = x ) for the X = 5 , 5 ⋅ P ( X = 5 ) = 5 ⋅ ( 0.25 ) = 1.25 Calculate the value of x ⋅ P ( X = x ) for the X = 6 , 6 ⋅ P ( X = 6 ) = 6 ⋅ ( 0.3056 ) = 1.8336 Display the values of x ⋅ P ( X = x ) in tabular form, x 1 2 3 4 5 6 P ( X = x ) 0.0278 0.0833 0.1389 0.1944 0.25 0.3056 x ⋅ P ( X = x ) 0.0278 0.1667 0.4167 0.7776 1.25 1.8336 Calculate the expected value as follows: μ = ∑ i = 1 n x i ⋅ P ( X = x i ) = 0.0278 + 0.1667 + 0.4167 + 0.7776 + 1.25 + 1.8336 ≈ 4.47 Calculate the value of ( x − μ ) for the X = 1 , by subtracting the expected value from the values of X. ( x − μ ) = ( 1 − 4

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Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8.4, Problem 19E

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To calculate: The expected value, the variance, and the standard deviation of the random variable X when two dice are rolled, and X is the higher number.

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Chapter 8.4, Problem 18E

Chapter 8.4, Problem 20E

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Question 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = parallel to the plane 5x + 2y + z = 1. 1+t, y2t, z = 43t and is (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y=1+t, and z = 2 – t. (e) The plane that contains the lines L₁ : x = 1 + t, y = 1 − t, z = = L2 x 2s, y = s, z = 2. 2t and

2 5x + 2–49 2 x+10x+21

5x 2x+y+ 3x + 3y 4 6

Chapter 8 Solutions

Finite Mathematics

Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 110, classify the random variable X...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - In Exercises 110, classify the random variable X...

Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - Prob. 13E Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - In Exercises 1118, (a) say what an appropriate...Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - The random variable X has the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - Prob. 23E Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - In Exercises 2128, give the probability...Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - 2010 Income Distribution up to $100,000 The...Ch. 8.1 - 2003 Income Distribution up to $100,000 Repeat...Ch. 8.1 - Population Age in Mexico The following chart shows...Ch. 8.1 - Population Age in the United States Repeat...Ch. 8.1 - 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Exercises 51 and 52 assume familiarity with...Ch. 8.3 - Exercises 51 and 52 assume familiarity with...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Elimination Tournaments In an elimination...Ch. 8.3 - Prob. 57E Ch. 8.3 - Prob. 58E Ch. 8.3 - Prob. 59E Ch. 8.3 - Insurance The Blue Sky Flight Insurance Company...Ch. 8.3 - Prob. 61E Ch. 8.3 - Prob. 62E Ch. 8.3 - Prob. 63E Ch. 8.3 - Prob. 64E Ch. 8.3 - Prob. 65E Ch. 8.3 - Prob. 66E Ch. 8.3 - Prob. 67E Ch. 8.3 - Prob. 68E Ch. 8.3 - Slim tells you that the population mean is just...Ch. 8.3 - Prob. 70E Ch. 8.3 - Prob. 71E Ch. 8.3 - Prob. 72E Ch. 8.3 - Prob. 73E Ch. 8.3 - Prob. 74E Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - In Exercises 18, compute the (sample) variance and...Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - Prob. 11E Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - Prob. 13E Ch. 8.4 - In Exercises 914, calculate the standard deviation...Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - In Exercises 1524, calculate the expected value,...Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Popularity Ratings In your bid to be elected class...Ch. 8.4 - Popularity Ratings Your candidacy for elected...Ch. 8.4 - Unemployment Following is a sample of unemployment...Ch. 8.4 - Unemployment Following is a sample of unemployment...Ch. 8.4 - Stock Market Gyrations Following is a sample of...Ch. 8.4 - Stock Market Gyrations Following is a sample of...Ch. 8.4 - Sport Utility Vehicles Following are highway...Ch. 8.4 - Sport Utility Vehicles Following are the city...Ch. 8.4 - Shopping Malls A survey of all the shopping malls...Ch. 8.4 - Prob. 34E Ch. 8.4 - 2010 Income Distribution up to $100,000 The...Ch. 8.4 - Prob. 36E Ch. 8.4 - Hispanic Employment: Male The following table...Ch. 8.4 - Hispanic Employment: Female Repeat Exercise 37,...Ch. 8.4 - Commerce You have been told that the average life...Ch. 8.4 - Commerce You have been told that the average life...Ch. 8.4 - Batmobiles The average life span of a Batmobile is...Ch. 8.4 - Spiderman Coupes The average life span of a...Ch. 8.4 - Teenage Pastimes According to a study,51 the...Ch. 8.4 - Prob. 44E Ch. 8.4 - Teenage Marketing In 2000, 22% of all teenagers in...Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.4 - Video Arcades Your company, Sonic Video, Inc., has...Ch. 8.4 - Prob. 49E Ch. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 51E Ch. 8.4 - Prob. 52E Ch. 8.4 - Prob. 53E Ch. 8.4 - Prob. 54E Ch. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 56E Ch. 8.4 - Prob. 57E Ch. 8.4 - Prob. 58E Ch. 8.4 - Prob. 59E Ch. 8.4 - Distribution of Wealth If we model after-tax...Ch. 8.4 - Prob. 61E Ch. 8.4 - Prob. 62E Ch. 8.4 - Prob. 63E Ch. 8.4 - Prob. 64E Ch. 8.4 - Prob. 65E Ch. 8.4 - Prob. 66E Ch. 8.4 - Prob. 67E Ch. 8.4 - Prob. 68E Ch. 8.4 - Prob. 69E Ch. 8.4 - Prob. 70E Ch. 8.4 - Prob. 71E Ch. 8.4 - Prob. 72E Ch. 8.4 - Prob. 73E Ch. 8.4 - Prob. 74E Ch. 8.4 - Prob. 75E Ch. 8.4 - Prob. 76E Ch. 8.4 - Prob. 77E Ch. 8.4 - Prob. 78E Ch. 8.4 - Prob. 79E Ch. 8.4 - Prob. 80E Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - In Exercises 18, Z is the standard normal...Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - In Exercises 914, X has a normal distribution with...Ch. 8.5 - 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Baseball The mean batting average in major league...Ch. 8.5 - Baseball The mean batting average in major league...Ch. 8.5 - Prob. 39E Ch. 8.5 - Marketing Your hot sauce company rates its sauce...Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Distribution of Income If we model after-tax...Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.5 - Prob. 57E Ch. 8.5 - Prob. 58E Ch. 8.5 - Aviation The probability of a plane crashing on a...Ch. 8.5 - Prob. 60E Ch. 8.5 - Prob. 61E Ch. 8.5 - Prob. 62E Ch. 8.5 - Prob. 63E Ch. 8.5 - Prob. 64E Ch. 8.5 - Prob. 65E Ch. 8.5 - Prob. 66E Ch. 8.5 - Prob. 67E Ch. 8.5 - Prob. 68E Ch. 8.5 - Prob. 69E Ch. 8.5 - Prob. 70E Ch. 8.5 - Prob. 71E Ch. 8.5 - Prob. 72E Ch. 8.5 - Prob. 73E Ch. 8.5 - Prob. 74E Ch. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - In Exercises 16, find the probability distribution...Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - A die is constructed in such a way that rolling a...Ch. 8 - Prob. 17RE Ch. 8 - Prob. 18RE Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Prob. 23RE Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - In Exercises 2934 the mean and standard deviation...Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 1CS Ch. 8 - Prob. 2CS Ch. 8 - Prob. 3CS Ch. 8 - Prob. 4CS Ch. 8 - Which of the following lists of data would you...Ch. 8 - Prob. 6CS Ch. 8 - Prob. 7CS Ch. 8 - Prob. 8CS

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The expected value, the variance, and the standard deviation of the random variable X when two dice are rolled, and X is the higher number.

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Chapter 8 Solutions