   Chapter 9.3, Problem 37E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Consumer Trends The number of coupons x used by a customer in a grocery store is a random variable with the probability density function f ( x ) = 2 x   +   1 12 , [ 0 ,   3 ] .Find the expected number of coupons a customer will use.

To determine

To calculate: The expected number of coupons a customer will use in the grocery store f(x)=2x+112with0x3

Explanation

Given information:

The number of coupons used by a customer in the grocery store is represented by the random variable x with a probability density f(x)=2x+112with0x3

Formula used:

If f(x) is the probability density function of a continuous random variable x over the interval [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

Calculation:

Consider given probability density equation:

f(x)=2x+112with0x3

The mean can be calculated as;

μ=E(x)=03xf(x)dx=03x

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