Explanation Definition used: The function f is a probability density function of a random variable X in the interval [ a , b ] if 1. f ( x ) ≥ 0 for all x in the interval [ a , b ] . 2. ∫ a b f ( x ) d x = 1 . Calculation: Consider, the given function f ( x ) = 1 27 ( 2 x + 4 ) in the interval [ 1 , 4 ] . It is given that, the value of x is in the interval [ 1 , 4 ] . It is observed that, the condition 1 holds, that is, f ( x ) ≥ 0 for the interval [ 1 , 4 ] . Next show that the condition 2 holds. ∫ 1 4 f ( x ) d x = ∫ 1 4 1 27 ( 2 x + 4 ) d x = 1 27 ∫ 1 4 2 x d x + 1 27 ∫ 1 4 4 d x = 1 27 [

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 11, Problem 16RE

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To decide: Whether the function f(x)=127(2x+4) in the interval [1,4] is probability density function or not.

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Chapter 11, Problem 15RE

Chapter 11, Problem 17RE

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Chapter 11 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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To decide: Whether the function f ( x ) = 1 27 ( 2 x + 4 ) in the interval [ 1 , 4 ] is probability density function or not.

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To decide: Whether the function f(x)=127(2x+4) in the interval [1,4] is probability density function or not.

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Chapter 11 Solutions