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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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.

Die Roll x is (a) the number of points when a four-sided die is rolled once and (b) the sum of the points when the four-sided die is rolled twice.

(a)

To determine

To calculate: The mean, variance and standard deviation of the number of points when a four-sided die is rolled once.

Explanation

Given Information:

A four-sided dice is rolled once.

Formula used:

The probability of random variable is given by

P(x)=Frequency of xTotal number of outcomes

The expected value or the mean of the random variable of the set of values of the discrete random variable consisting of m different values is given by

Mean=x1P(x1)+x2P(x2)+...+xmP(xm)

The variance is given by

V(x)=(x1μ)2P(x1)+(x2μ)2P(x2)+...+(xmμ)2P(xm)

And the standard deviation is given by

σ=V(x)

Calculation:

Consider the statement,

A four-sided dice is rolled once.

Let S be the sample space. Then, S={1,2,3,4}.

So, number of possible outcomes is 4.

Frequency of each possible outcome is,

Random variable,x1234Frequency of x, n(x)1111

Then the probability of getting a number 1 will be

P(x1)=Frequency of x1Total number of outcomes=116

The probability of getting a number 2 will be

P(x2)=Frequency of x2Total number of outcomes=116

The probability of getting a number 3 will be

P

(b)

To determine

To calculate: The mean, variance and the standard deviation of sum of the points when a four-sided die is rolled twice.

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