Explanation Given Information: The probability distribution: x 0 1 2 3 4 P ( x ) 1 10 3 10 2 10 3 10 1 10 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 0 1 2 3 4 P ( x ) 1 10 3 10 2 10 3 10 1 10 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 ) = ( 0 ) ( 1 10 ) + ( 1 ) ( 3 10 ) + ( 2 ) ( 2 10 ) + ( 3 ) ( 3 10 ) + ( 4 ) ( 1 10 ) = 3 + 4 + 9 + 4 10 = 20 10 = 2 Thus, the expected value is E ( x ) = 2

WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term

10th Edition

ISBN: 9781337652308

Author: Ron Larson

Publisher: Brooks Cole

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Chapter 9, Problem 13RE

To determine

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

x

0

1

2

3

4

P(x)

110

310

210

310

110

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Chapter 9, Problem 12RE

Chapter 9, Problem 14RE

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 9 Solutions

WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term

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The expected value, variance and standard deviation of the probability distribution: x 0 1 2 3 4 P ( x ) 1 10 3 10 2 10 3 10 1 10

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

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

x

0

1

2

3

4

P(x)

110

310

210

310

110

Want to see the full answer?

Chapter 9 Solutions

The expected value, variance and standard deviation of the probability distribution: x 0 1 2 3 4 P ( x ) 1 10 3 10 2 10 3 10 1 10

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

Concept explainers

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To calculate: The expected value, variance and standard deviation of the probability distribution: x 0 1 2 3 4 P(x) 110 310 210 310 110

Want to see the full answer?

Chapter 9 Solutions

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

x

0

1

2

3

4

P(x)

110

310

210

310

110