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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 Expected Value, Variance, and Standard Deviation In Exercises 23–26, find the expected value, variance, and standard deviation for the given probability distribution. See Examples 4, 5, and 6.

x 1 2 3 4 5
P(x) 4 10 2 10 2 10 1 10 1 10

To determine

To calculate: The value of expected value, variance and standard deviation for given probability distribution.

x 1 2 3 4 5
P(x) 410 210 210 110 110
Explanation

Given Information:

The random variable and their probability are given as

x 1 2 3 4 5
P(x) 410 210 210 110 110

Formula used:

If the set of values of a discrete random variable consist in district values x1,x2,,xn then

E(x)=x1P(x1)+x2P(x2)++xnP(xn)

If mean μ=E(x) then variance

V(x)=(x1μ)2P(x1)+(x2μ)2P(x2)++(xnμ)2P(xn)

And the standard deviation is,

σ=V(x)

Calculation:

Consider the given information

x1=1P(x1)=410x2=2P(x2)=210

And,

x3=3P(x3)=210x4=4P(x4)=110

And,

x5=5P(x5)=110

Consider the primary equation and substitute the given values

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