(a) To determine To find: The longest time within the predator will be 90% certain to find a prey. Explanation Given: The mean exponentially distributed with 25. Definition used: Exponential Distribution : If X is a random variable with probability density function f ( x ) = a e − a x for x in [ 0 , ∞ ) . Then mean is, E ( X ) = μ = 1 a . The standard deviation is σ = 1 a . Formula used: Probability density function on ( − ∞ , ∞ ) : If f is a probability density function for a random variable X in the interval ( − ∞ , ∞ ) , then 1. P ( x ≤ b ) = P ( x < b ) = ∫ − ∞ b f ( x ) d x 2. P ( x ≥ a ) = P ( x > a ) = ∫ a ∞ f ( x ) d x 3. P ( − ∞ < x < ∞ ) = ∫ − ∞ ∞ f ( x ) d x = 1 . Calculation: It is given that, the exponential distribution of the function is f ( x ) = a e − a x with mean 25. Use above mentioned definition as follows. E ( X ) = 25 1 a = 25 a = 1 25 = 0.04 Therefore, the exponential distribution is f ( x ) = 0 (b) To determine To find: The probability that the predator will have to spend more than 1 hour looking for a prey.

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 11.3, Problem 43E

(a)

To determine

To find: The longest time within the predator will be 90% certain to find a prey.

(b)

To determine

To find: The probability that the predator will have to spend more than 1 hour looking for a prey.

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Chapter 11.3, Problem 42E

Chapter 11.3, Problem 44E

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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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