Explanation Given Information: The function f ( x ) = 1 8 e − x / 8 over the interval [ 0 , 8 ] . Graph: Consider the provided function f ( x ) = 1 8 e − x / 8 . Use the ti-83 graphing calculator to construct the graph of the function. Step 1: Open the ti-83 graphing calculator. Step 2: Press [ y = ] and enter the function Y 1 = 1 8 e − x / 8 . Step 3: Press the [ window ] key and adjust the scale. X min = 0 X max = 8 X s c l = 1 And, Y min = 0 Y max = 0.25 Y s c l = 0.01 Step 4: Press the [ graph ] key. The graph of the function f ( x ) = 1 8 e − x / 8 is obtained as, Consider the provided function f ( x ) = 1 8 e − x / 8 over the interval [ 0 , 8 ] . A function f of a continuous random variable x in the interval [ a , b ] is a probability density function if it is nonnegative and continuous on the interval [ a , b ] . And, ∫ a b f ( x ) d x = 1 For x = 8 in the interval [ 0 , 8 ] , the function is evaluated as, f ( 8 ) = 1 8 e − 8 / 8 = 1 8 e − 1 = 0.3679 8 ≈ 0.046 The function f is continuous and nonnegative for all values on the interval [ 0 , 8 ] . Since, the provided function is a constant function and so the function f is continuous and nonnegative for all values on the interval [ 0 , 8 ] . Now, show that ∫ a b f ( x ) d x = 1

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 9, Problem 29RE

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To graph: The function using a graphing utility and determine whether the function f(x)=18e−x/8 represents a probability density function over the interval [0,8].

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Chapter 9, Problem 28RE

Chapter 9, Problem 30RE

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CP Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1SWU Ch. 9.1 - Prob. 2SWU Ch. 9.1 - Prob. 3SWU Ch. 9.1 - Prob. 4SWU

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Knowledge Booster

To graph: The function using a graphing utility and determine whether the function f ( x ) = 1 8 e − x / 8 represents a probability density function over the interval [ 0 , 8 ] .

Solution Summary: The author analyzes the graph of the function f(x)=18e-x/8 using a graphing utility.

To graph: The function using a graphing utility and determine whether the function f(x)=18e−x/8 represents a probability density function over the interval [0,8].

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Chapter 9 Solutions