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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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Cost The daily cost x (in dollars) of electricity in a city is a random variable with the probability density function

f ( x ) =   0.28 e 028 x ,   [ 0 ,   ) .

Find the expected daily cost of electricity in the city.

To determine

To calculate: The expected daily cost of electricity consumption in a city with the probability density function f(x)=0.28e0.28x where ‘x’ is the daily cost of electricity consumption with 0x

Explanation

Given information:

The daily cost of electricity consumption represented by the random variable x has a probability density function f(x)=0.28e0.28xwith0x

Formula used:

If ‘f’ is the probability density function of a continuous random variable x over the interval a, [a,b], then the expected value or mean is given by;

μ=E(x)=abxf(x)dx

And, the median ‘x’ is the number m such that;

amf(x)dx=0.5

The formula for integration by parts is;

uvdx=uvdxdudx[vdx]dx

Calculation:

Consider given probability density function :

f(x)=0.28e0.28xwith0x

Consider the primary equation,

μ=E(x)=0xf(x)dx=0x×0.280.28xdx=0.280xe0.28xdx

Use integration by parts formula uvdx=uvdxdudx[vdx]dx

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