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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 43RE

Textbook Problem

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**Finding Expected Value, Variance, and Standard Deviation** In Exercises 39–44, use the given probability density function over the indicated interval to find the (a) expected value, (b) variance, and (c) standard deviation of the random variable. (d) Then sketch the graph of the probability density function and locate the mean on the graph.

**(a)**

To determine

**To calculate:** The expected value of probability density function

**Given Information:**

The probability density function is,

**Formula used:**

The expected value *f* for a continuous random variable *x* over the interval

The simple power rule of integration,

The Fundamental theorem of calculus for definite integral of a function *f* on a closed interval

**Calculation:**

Consider the provided probability density function,

Use the definition of expected value for the provided probability density function,

Substitute 0 for *a*, 3 for *b* and

**(b)**

To determine

**To calculate:** The variance of probability density function

**(c)**

To determine

**To calculate:** The standard deviation of probability density function

**(d)**

To determine

**To graph:** The probability density function

Calculus: An Applied Approach (MindTap Course List)

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