Explanation Given Information: The probability distribution: x − 2 − 1 0 1 2 P ( x ) 0.141 0.305 0.257 0.063 0.234 Formula used: If a discrete random variable takes the values { x 1 , x 2 , ⋯ , x m } , then the expected value of the random variable is defined as, E ( x ) = x 1 P ( x 1 ) + x 2 P ( x 2 ) + ⋯ + x m P ( x m ) Variance of the random variable is defined as, V ( x ) = ( x 1 − μ ) 2 P ( x 1 ) + ( x 2 − μ ) 2 P ( x 2 ) + ⋯ + ( x m − μ ) 2 P ( x m ) The standard deviation of the random variable is defined as, σ = V ( x ) Calculation: Consider the provided probability distribution. x − 2 − 1 0 1 2 P ( x ) 0.141 0.305 0.257 0.063 0.234 First use the provided probability distribution and the expected value formula E ( x ) = x 1 P ( x 1 ) + x 2 P ( x 2 ) + ⋯ + x m P ( x m ) to calculate the expected value of the probability distribution. So, the expected value is calculated as, E ( x ) = ( − 2 ) ( 0.141 ) + ( − 1 ) ( 0

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 9, Problem 6TYS

To determine

To calculate: The expected value, variance and standard deviation of the probability distribution:

x −2 −1 0 1 2

P(x) 0.141 0.305 0.257 0.063 0.234

Expert Solution & Answer

Chapter 9 Solutions

Calculus: An Applied Approach (Providence College: MTH 109)

Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CP Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1SWU Ch. 9.1 - Prob. 2SWU Ch. 9.1 - Prob. 3SWU Ch. 9.1 - Prob. 4SWU

Ch. 9.1 - Prob. 5SWU Ch. 9.1 - Prob. 6SWU Ch. 9.1 - Prob. 7SWU Ch. 9.1 - Prob. 8SWU Ch. 9.1 - Prob. 9SWU Ch. 9.1 - Prob. 10SWU Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Children The table shows the probability...Ch. 9.1 - Prob. 21E Ch. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Prob. 23E 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 - Prob. 29E Ch. 9.1 - Personal Income The probability distribution of...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Baseball A baseball fan examined the record of a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.2 - Prob. 1CP Ch. 9.2 - Prob. 2CP Ch. 9.2 - Prob. 3CP Ch. 9.2 - Prob. 4CP Ch. 9.2 - Prob. 5CP Ch. 9.2 - Prob. 1SWU Ch. 9.2 - Prob. 2SWU Ch. 9.2 - Prob. 3SWU Ch. 9.2 - Prob. 4SWU Ch. 9.2 - Prob. 5SWU Ch. 9.2 - Prob. 6SWU Ch. 9.2 - Prob. 7SWU Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Demand The daily demand for gasoline x (in...Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 34E Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Demand The weekly demand x (in tons) for a certain...Ch. 9.2 - Prob. 39E Ch. 9.3 - Prob. 1CP Ch. 9.3 - Find the variance and standard deviation of the...Ch. 9.3 - Use a symbolic integration utility to find the...Ch. 9.3 - Prob. 4CP Ch. 9.3 - Prob. 5CP Ch. 9.3 - Prob. 6CP Ch. 9.3 - Prob. 7CP Ch. 9.3 - Prob. 1SWU Ch. 9.3 - Prob. 2SWU Ch. 9.3 - Prob. 3SWU Ch. 9.3 - Prob. 4SWU Ch. 9.3 - Prob. 5SWU Ch. 9.3 - Prob. 6SWU Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 13E Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Prob. 15E Ch. 9.3 - Using two Methods In Exercises 1316, find the...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Prob. 34E Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Consumer Trends The number of coupons x used by a...Ch. 9.3 - Prob. 38E Ch. 9.3 - Prob. 39E Ch. 9.3 - Prob. 40E Ch. 9.3 - Transportation The arrival time t (in minutes) of...Ch. 9.3 - Prob. 42E Ch. 9.3 - Prob. 43E Ch. 9.3 - Prob. 44E Ch. 9.3 - Prob. 45E Ch. 9.3 - License Renewal The waiting time t (in minutes) at...Ch. 9.3 - Demand The daily demand x for a certain product...Ch. 9.3 - Prob. 48E Ch. 9.3 - Demand The daily demand x for water (in millions...Ch. 9.3 - Prob. 50E Ch. 9.3 - Prob. 54E Ch. 9.3 - Prob. 55E Ch. 9.3 - Education For high school graduates from 2012...Ch. 9.3 - Prob. 57E Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Revenue A publishing company introduces a new...Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Waiting Time The waiting time t (in minutes) for...Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 1TYS Ch. 9 - Prob. 2TYS Ch. 9 - Prob. 3TYS Ch. 9 - Prob. 4TYS Ch. 9 - Prob. 5TYS Ch. 9 - Prob. 6TYS Ch. 9 - Prob. 7TYS Ch. 9 - Prob. 8TYS Ch. 9 - Prob. 9TYS Ch. 9 - Prob. 10TYS Ch. 9 - Prob. 11TYS Ch. 9 - Prob. 12TYS Ch. 9 - Prob. 13TYS Ch. 9 - Prob. 14TYS Ch. 9 - Prob. 15TYS Ch. 9 - Prob. 16TYS

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The expected value, variance and standard deviation of the probability distribution: x − 2 − 1 0 1 2 P ( x ) 0.141 0.305 0.257 0.063 0.234

Solution Summary: The author calculates the expected value, variance, and standard deviation of the probability distribution.

Concept explainers

Videos

To calculate: The expected value, variance and standard deviation of the probability distribution:

x −2 −1 0 1 2

P(x) 0.141 0.305 0.257 0.063 0.234

Chapter 9 Solutions

The expected value, variance and standard deviation of the probability distribution: x − 2 − 1 0 1 2 P ( x ) 0.141 0.305 0.257 0.063 0.234

Solution Summary: The author calculates the expected value, variance, and standard deviation of the probability distribution.

Concept explainers

Videos

To calculate: The expected value, variance and standard deviation of the probability distribution: x −2 −1 0 1 2 P(x) 0.141 0.305 0.257 0.063 0.234

Chapter 9 Solutions

To calculate: The expected value, variance and standard deviation of the probability distribution:

x −2 −1 0 1 2

P(x) 0.141 0.305 0.257 0.063 0.234