Calculus: An Applied Approach (Min...

10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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Finding Mean, Variance, and Standard Deviation In Exercises 27 and 28, find the mean, variance, and standard deviation of the discrete random variable x. See Examples 4, 5, and 6.

Spinner A spinner is divided into three equal sections labeled 1, 2. and 3. x is (a) the number landed on when the spinner is spun once and (b) the sum of the numbers landed on when the spinner is spun twice.

(a)

To determine

To calculate: The mean, variance and standard deviation of the discrete random variable x where x is the number landed on spinner when the spinner is spun once.

Explanation

Given Information:

A spinner is divided into three equal sections named 1, 2, 3.

Formula used:

Probability distribution:

The probability of a random variable x is

P(x)=Frequency of xNumber of outcomes in S=n(x)n(S)

Expected value:

If y is a discrete random variable with values y1,y2,…,yn then the mean μ of the distribution is the expected value of y given by

E(y)=y1P(y1)+y2P(y2)+…+ynP(yn)

Where the expected value of y is denoted by E(y).

Variance:

Consider a random variable whose possible values are {x1,x2,x3,…,xm} with a mean of μ. Then, the variance of the random variable is,

V(x)=(x1−μ)2P(x1)+(x2−μ)2P(x2)+…+(xm−μ)2P(xm)

Standard deviation:

The standard deviation of the random variable is

σ=V(x)

Calculation:

A spinner is divided into three equal sections named 1, 2, 3.

Let S be the sample space. Then, S={1,2,3}.

So, a number of possible outcomes is 3.

The frequency of each possible outcome is,

Random variable,x123Frequency of x, n(x)111

So, the probability that 1 land on when the spinner is spun once is,

P(1)=Frequency of 1Number of outcomes in S=n(1)n(S)=13

The probability that 2 land on when the spinner is spun once is,

P(2)=Frequency of 2Number of outcomes in S=n(2)n(S)=

(b)

To determine

To calculate: The mean, variance and standard deviation of the discrete random variable x where x is the sum of the numbers landed on spinner when the spinner is spun twice.

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Chapter 9 Solutions

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Sect-9.1 P-1CP Sect-9.1 P-2CP Sect-9.1 P-3CP Sect-9.1 P-4CP Sect-9.1 P-5CP Sect-9.1 P-6CP Sect-9.1 P-1SWU Sect-9.1 P-2SWU Sect-9.1 P-3SWU Sect-9.1 P-4SWU

Sect-9.1 P-5SWU Sect-9.1 P-6SWU Sect-9.1 P-7SWU Sect-9.1 P-8SWU Sect-9.1 P-9SWU Sect-9.1 P-10SWU Sect-9.1 P-1E Sect-9.1 P-2E Sect-9.1 P-3E Sect-9.1 P-4E Sect-9.1 P-5E Sect-9.1 P-6E Sect-9.1 P-7E Sect-9.1 P-8E Sect-9.1 P-9E Sect-9.1 P-10E Sect-9.1 P-11E Sect-9.1 P-12E Sect-9.1 P-13E Sect-9.1 P-14E Sect-9.1 P-15E Sect-9.1 P-16E Sect-9.1 P-17E Sect-9.1 P-18E Sect-9.1 P-19E Sect-9.1 P-20E Sect-9.1 P-21E Sect-9.1 P-22E Sect-9.1 P-23E Sect-9.1 P-24E Sect-9.1 P-25E Sect-9.1 P-26E Sect-9.1 P-27E Sect-9.1 P-28E Sect-9.1 P-29E Sect-9.1 P-30E Sect-9.1 P-31E Sect-9.1 P-32E Sect-9.1 P-33E Sect-9.1 P-35E Sect-9.1 P-36E Sect-9.1 P-37E Sect-9.1 P-38E Sect-9.2 P-1CP Sect-9.2 P-2CP Sect-9.2 P-3CP Sect-9.2 P-4CP Sect-9.2 P-5CP Sect-9.2 P-1SWU Sect-9.2 P-2SWU Sect-9.2 P-3SWU Sect-9.2 P-4SWU Sect-9.2 P-5SWU Sect-9.2 P-6SWU Sect-9.2 P-7SWU Sect-9.2 P-1E Sect-9.2 P-2E Sect-9.2 P-3E Sect-9.2 P-4E Sect-9.2 P-5E Sect-9.2 P-6E Sect-9.2 P-7E Sect-9.2 P-8E Sect-9.2 P-9E Sect-9.2 P-10E Sect-9.2 P-11E Sect-9.2 P-12E Sect-9.2 P-13E Sect-9.2 P-14E Sect-9.2 P-15E Sect-9.2 P-16E Sect-9.2 P-17E Sect-9.2 P-18E Sect-9.2 P-19E Sect-9.2 P-20E Sect-9.2 P-21E Sect-9.2 P-22E Sect-9.2 P-23E Sect-9.2 P-24E Sect-9.2 P-25E Sect-9.2 P-26E Sect-9.2 P-27E Sect-9.2 P-28E Sect-9.2 P-29E Sect-9.2 P-30E Sect-9.2 P-31E Sect-9.2 P-32E Sect-9.2 P-33E Sect-9.2 P-34E Sect-9.2 P-35E Sect-9.2 P-36E Sect-9.2 P-37E Sect-9.2 P-38E Sect-9.2 P-39E Sect-9.3 P-1CP Sect-9.3 P-2CP Sect-9.3 P-3CP Sect-9.3 P-4CP Sect-9.3 P-5CP Sect-9.3 P-6CP Sect-9.3 P-7CP Sect-9.3 P-1SWU Sect-9.3 P-2SWU Sect-9.3 P-3SWU Sect-9.3 P-4SWU Sect-9.3 P-5SWU Sect-9.3 P-6SWU Sect-9.3 P-1E Sect-9.3 P-2E Sect-9.3 P-3E Sect-9.3 P-4E Sect-9.3 P-5E Sect-9.3 P-6E Sect-9.3 P-7E Sect-9.3 P-8E Sect-9.3 P-9E Sect-9.3 P-10E Sect-9.3 P-11E Sect-9.3 P-12E Sect-9.3 P-13E Sect-9.3 P-14E Sect-9.3 P-15E Sect-9.3 P-16E Sect-9.3 P-17E Sect-9.3 P-18E Sect-9.3 P-19E Sect-9.3 P-20E Sect-9.3 P-21E Sect-9.3 P-22E Sect-9.3 P-23E Sect-9.3 P-24E Sect-9.3 P-25E Sect-9.3 P-26E Sect-9.3 P-27E Sect-9.3 P-28E Sect-9.3 P-29E Sect-9.3 P-30E Sect-9.3 P-31E Sect-9.3 P-32E Sect-9.3 P-33E Sect-9.3 P-34E Sect-9.3 P-35E Sect-9.3 P-36E Sect-9.3 P-37E Sect-9.3 P-38E Sect-9.3 P-39E Sect-9.3 P-40E Sect-9.3 P-41E Sect-9.3 P-42E Sect-9.3 P-43E Sect-9.3 P-44E Sect-9.3 P-45E Sect-9.3 P-46E Sect-9.3 P-47E Sect-9.3 P-48E Sect-9.3 P-49E Sect-9.3 P-50E Sect-9.3 P-54E Sect-9.3 P-55E Sect-9.3 P-56E Sect-9.3 P-57E Ch-9 P-1RE Ch-9 P-2RE Ch-9 P-3RE Ch-9 P-4RE Ch-9 P-5RE Ch-9 P-6RE Ch-9 P-7RE Ch-9 P-8RE Ch-9 P-9RE Ch-9 P-10RE Ch-9 P-11RE Ch-9 P-12RE Ch-9 P-13RE Ch-9 P-14RE Ch-9 P-15RE Ch-9 P-16RE Ch-9 P-17RE Ch-9 P-18RE Ch-9 P-19RE Ch-9 P-20RE Ch-9 P-21RE Ch-9 P-22RE Ch-9 P-23RE Ch-9 P-24RE Ch-9 P-25RE Ch-9 P-26RE Ch-9 P-27RE Ch-9 P-28RE Ch-9 P-29RE Ch-9 P-30RE Ch-9 P-31RE Ch-9 P-32RE Ch-9 P-33RE Ch-9 P-34RE Ch-9 P-35RE Ch-9 P-36RE Ch-9 P-37RE Ch-9 P-38RE Ch-9 P-39RE Ch-9 P-40RE Ch-9 P-41RE Ch-9 P-42RE Ch-9 P-43RE Ch-9 P-44RE Ch-9 P-45RE Ch-9 P-46RE Ch-9 P-47RE Ch-9 P-48RE Ch-9 P-49RE Ch-9 P-50RE Ch-9 P-51RE Ch-9 P-52RE Ch-9 P-53RE Ch-9 P-54RE Ch-9 P-55RE Ch-9 P-56RE Ch-9 P-57RE Ch-9 P-58RE Ch-9 P-59RE Ch-9 P-60RE Ch-9 P-61RE Ch-9 P-62RE Ch-9 P-1TYS Ch-9 P-2TYS Ch-9 P-3TYS Ch-9 P-4TYS Ch-9 P-5TYS Ch-9 P-6TYS Ch-9 P-7TYS Ch-9 P-8TYS Ch-9 P-9TYS Ch-9 P-10TYS Ch-9 P-11TYS Ch-9 P-12TYS Ch-9 P-13TYS Ch-9 P-14TYS Ch-9 P-15TYS Ch-9 P-16TYS

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Calculus: An Applied Approach (Min...

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Calculus Calculus: An Applied Approach (MindTap Course List)10th Edition