Question

The amount of time (in minutes) a shopper spends browsing in the magazine section of a supermarket is a continuous random variable with probability density function $$f(t)=\frac{2}{25} t \quad(0 \leq t \leq 5)$$ How much time is a shopper chosen at random expected to spend in the magazine section?

Name: Problem 15, Chapter 10: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-22T13:39:38-08:00
Duration: 1 min 12 s
Channel: Wendi Zhao
Description: The amount of time (in minutes) a shopper spends browsing in the magazine section of a supermarket is a continuous random variable with probability density function f(t)=(2)/(25) t (0 ≤t ≤5) How much time is a shopper chosen at random expected to spend in the magazine section?

   The amount of time (in minutes) a shopper spends browsing in the magazine section of a supermarket is a continuous random variable with probability density function $$f(t)=\frac{2}{25} t \quad(0 \leq t \leq 5)$$ 
How much time is a shopper chosen at random expected to spend in the magazine section?

Applied Calculus for the Managerial, Life, and Social Sciences

Soo T. Tan 10th Edition

Chapter 10, Problem 15

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Solved by Expert Wendi Zhao

05/22/2021

Step 1

In this case, the expectation E(T) is given by: \[E(T) = \int_{0}^{5} t \cdot f(t) dt\] Show more…

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The amount of time (in minutes) a shopper spends browsing in the magazine section of a supermarket is a continuous random variable with probability density function $$f(t)=\frac{2}{25} t \quad(0 \leq t \leq 5)$$ How much time is a shopper chosen at random expected to spend in the magazine section?

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Key Concepts

Probability Density Function (PDF)

A function that describes the relative likelihood of a continuous random variable taking on a particular value. The PDF is defined such that the probability that the variable falls within a certain interval is given by the integral of the PDF over that interval, and overall, the function must integrate to 1 over its entire range.

Expected Value for a Continuous Random Variable

The expected value is the theoretical mean of the distribution, representing the long-run average outcome if the random experiment were repeated many times. For continuous random variables, it is computed by integrating the product of the variable and its probability density function over its range.

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