Explanation Given Information: The random variable X is the number that is selected randomly from the set { 1 , 2, 3, 4 } . Formula used: The formula to compute the expected value is, μ = E ( X ) = ∑ i = 1 n x i P ( X = x i ) The term P ( X = x ) denotes the probability of the event X = x . The probability of an event is calculated using the formula, P ( X ) = Number of favorable outcomes Total number of outcomes The variance is given by the formula, σ 2 = ∑ i = 1 n ( x i − μ ) 2 P ( X = x i ) The standard deviation of X is given by the formula, σ = σ 2 Calculation: Consider the set of four values { 1 , 2, 3, 4 } . Calculate the probability of selecting 1 , P ( X ) = Number of favorable outcomes Total number of outcomes = 1 4 Calculate the probability of selecting 2 , P ( X ) = Number of favorable outcomes Total number of outcomes = 1 4 Calculate the probability of selecting 3 , P ( X ) = Number of favorable outcomes Total number of outcomes = 1 4 Calculate the probability of selecting 4 , P ( X ) = Number of favorable outcomes Total number of outcomes = 1 4 The probability distribution table is as follows: x 1 2 3 4 P ( X = x ) 1 / 4 1 / 4 1 / 4 1 / 4 Calculate the value of x ⋅ P ( X = x ) for X = 1 , x ⋅ P ( X = x ) = 1 ⋅ ( 1 / 4 ) = 1 / 4 Calculate the value of x ⋅ P ( X = x ) for X = 2 , x ⋅ P ( X = x ) = 2 ⋅ ( 1 / 4 ) = 2 / 4 Calculate the value of x ⋅ P ( X = x ) for X = 3 , x ⋅ P ( X = x ) = 3 ⋅ ( 1 / 4 ) = 3 / 4 Calculate the value of x ⋅ P ( X = x ) for X = 4 , x ⋅ P ( X = x ) = 4 ⋅ ( 1 / 4 ) = 4 / 4 Display the values of x ⋅ P ( X = x ) for all the values of X in tabular form, x 1 2 3 4 P ( X = x ) 1 / 4 1 / 4 1 / 4 1 / 4 x ⋅ P ( X = x ) 1 / 4 2 / 4 3 / 4 4 / 4 Calculate the expected value as follows: E ( X ) = ∑ i = 1 n x i ⋅ P ( X = x i ) = 1 4 + 2 4 + 3 4 + 4 4 = ( 1 + 2 + 3 + 4 ) 4 = 10 4 Simplify further, E ( X ) = 2.5 Thus, the expected value of X is 2.5 . Calculate the value of σ 2 using the formula σ 2 = ∑ i = 1 n ( x i − μ ) 2 P ( X = x i ) , Calculate the value of ( x − μ ) for X = 1 , ( x − μ ) = 1 − 2

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 9.4, Problem 16E

To determine

To calculate: The expected value, variance and standard deviation of the random variable X= the number selected at random from the set {1, 2, 3, 4}.

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Chapter 9.4, Problem 15E

Chapter 9.4, Problem 17E

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Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - Prob. 2E Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - Prob. 5E Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - Prob. 7E Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - Prob. 16E Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - 2010 Income Distribution up to $100,000 The...Ch. 9.1 - 2003 Income Distribution up to $100,000 Repeat...Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Housing Prices Going into the Real Estate Bubble...Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Car Purchases To persuade his parents to...Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - 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Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - Prob. 17E Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - Prob. 23E Ch. 9.5 - Prob. 24E Ch. 9.5 - Prob. 25E Ch. 9.5 - Prob. 26E Ch. 9.5 - SAT Scores SAT test scores are normally...Ch. 9.5 - Prob. 28E Ch. 9.5 - Prob. 29E Ch. 9.5 - Prob. 30E Ch. 9.5 - IQ Scores IQ scores (as measured by the...Ch. 9.5 - Prob. 32E Ch. 9.5 - Prob. 33E Ch. 9.5 - Prob. 34E Ch. 9.5 - Prob. 35E Ch. 9.5 - Prob. 36E Ch. 9.5 - Baseball The mean batting average in major league...Ch. 9.5 - Prob. 38E Ch. 9.5 - Marketing Your pickle company rates its pickles on...Ch. 9.5 - Prob. 40E Ch. 9.5 - Prob. 41E Ch. 9.5 - Prob. 42E Ch. 9.5 - Prob. 43E Ch. 9.5 - Prob. 44E Ch. 9.5 - Prob. 45E Ch. 9.5 - Prob. 46E Ch. 9.5 - Prob. 47E Ch. 9.5 - Prob. 48E Ch. 9.5 - Prob. 49E Ch. 9.5 - Prob. 50E Ch. 9.5 - Prob. 51E Ch. 9.5 - Prob. 52E Ch. 9.5 - Prob. 53E Ch. 9.5 - Prob. 54E Ch. 9.5 - Prob. 55E Ch. 9.5 - Prob. 56E Ch. 9.5 - Prob. 57E Ch. 9.5 - 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The expected value, variance and standard deviation of the random variable X = the number selected at random from the set { 1 , 2, 3, 4 } .

Solution Summary: The author calculates the expected value, variance, and standard deviation of the random variable X= the number selected at random from the set.

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To calculate: The expected value, variance and standard deviation of the random variable X= the number selected at random from the set {1, 2, 3, 4}.

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Chapter 9 Solutions