Explanation Formula used: If X is an exponential random variable, then the probability density function is f ( x ) = { ( 1 λ ) e − x λ if x ≥ 0 0 otherwise . The respective cumulative distribution function is F ( x ) = { 1 − e − x λ if x ≥ 0 0 otherwise . Calculation: Given that X is exponentially distributed with λ = 1 4 . Substitute λ = 1 4 in the above formula to obtain the probability density function. f ( x ) = { ( 1 ( 1 4 ) ) e − x ( 1 4 ) if x ≥ 0 0 otherwise = { 4 e − 4 x if x ≥ 0 0

17th Edition

ISBN: 9781323520192

Author: Pearson

Publisher: PEARSON C

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 11.4, Problem 4E

To determine

To find: The probability density function f and the associated cumulative distribution function F for the exponential distributed random variable X with λ=14.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.4, Problem 3E

Chapter 11.4, Problem 5E

Students have asked these similar questions

Let g(x) = f(t) dt, where f is the function whose graph is shown. y 5 f 20 30 t (a) Evaluate g(x) for x = 0, 5, 10, 15, 20, 25, and 30. g(0) = g(5) = g(10) = g(15) =| g(20) = g(25) = g(30) = (b) Estimate g(35). (Use the midpoint to get the most precise estimate.) g(35) = (c) Where does g have a maximum and a minimum value? minimum x= maximum x=

Question Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.) x+6+ -2x²+3x-2 f(x) -2x-1 if x-5 if -−5≤ x ≤ 6 3 if x 6

Question Given the following piecewise function, evaluate lim f(x). (If the limit does not exist, enter DNE.) x-3 Provide your answer below: x² + 3x 3 if x-3 f(x) -3 if -3x -2x²+2x-1 6 if x 6

Chapter 11 Solutions

FIN 108 ISU LOOSE >IP<

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The probability density function f and the associated cumulative distribution function F for the exponential distributed random variable X with λ = 1 4 .

Solution Summary: The author explains the probability density function f and cumulative distribution function F for the exponential distributed random variable X with lambda =14.

Concept explainers

Videos

To find: The probability density function f and the associated cumulative distribution function F for the exponential distributed random variable X with λ=14.

Want to see the full answer?

Chapter 11 Solutions