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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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Personal Income The probability distribution of the random variable x, the annual income of a family (in thousands of dollars) in a certain section of a large city, is shown in the table. Find E(x) and α .

x 30 40 50 60 80
P(x) 0.10 0.20 0.50 0.15 0.05

To determine

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

x 30 40 50 60 80
P(x) 0.10 0.20 0.50 0.15 0.05
Explanation

Given Information:

The random variable and their probability are given as,

x 30 40 50 60 80
P(x) 0.10 0.20 0.50 0.15 0.05

Formula used:

In case of, 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,

σ=V(x)

Calculation:

Consider the given information,

x1=30P(x1)=0.10x2=40P(x2)=0.20

And,

x3=50P(x3)=0

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