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a) A random variable X has an exponential distribution with probability density function given by f(x) = {ledx; for x2 0 10 ,elsewhere

a) A random variable X has an exponential distribution with probability density function given by f(x) = {ledx; for x2 0 10 ,elsewhere

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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a) A random variable X has an exponential distribution with probability density function given by f(x) = {ledx; for x 2 0 lo ,elsewhere Find the 75th percentile of X. b) A certain brand of light bulb has a lifespan which is exponentially distribution with a mean of 35 days. 1. What is the probability that a randomly selected light bulb of this brand will last more than 45 days? II. If it is known that a light bulb has already lasted more than 25 days, what is the probability that it will at least last for an additional 50 days. (Hint: Memoryless Property) c) Suppose that the amount of time it takes for someone to finish a task, denoted by X, has the uniform distribution between 20 and 80 minutes. 1. Write a suitable probability density function for the time it takes someone to finish the task. II. Using the density function in (1) above derive the mean of X. II. Derive the variance of X using the results obtained in (I) and (I) above. IV. Find the probability that an individual takes between 30 and 75 minutes to finish the task.
Transcribed Image Text:a) A random variable X has an exponential distribution with probability density function given by f(x) = {ledx; for x 2 0 lo ,elsewhere Find the 75th percentile of X. b) A certain brand of light bulb has a lifespan which is exponentially distribution with a mean of 35 days. 1. What is the probability that a randomly selected light bulb of this brand will last more than 45 days? II. If it is known that a light bulb has already lasted more than 25 days, what is the probability that it will at least last for an additional 50 days. (Hint: Memoryless Property) c) Suppose that the amount of time it takes for someone to finish a task, denoted by X, has the uniform distribution between 20 and 80 minutes. 1. Write a suitable probability density function for the time it takes someone to finish the task. II. Using the density function in (1) above derive the mean of X. II. Derive the variance of X using the results obtained in (I) and (I) above. IV. Find the probability that an individual takes between 30 and 75 minutes to finish the task.
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