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Problem 16 A company makes a certain device. We are interested in the lifetime of the device. It is estimated that around 2% of the devices are defective from the start so they have a lifetime of 0 years. If a device is not defective, then the lifetime of the device is exponentially distributed with a parameter A = 2 years. Let X be the lifetime of a randomly chosen device. a. Find the generalized PDF of X. b. Find P(X > 1). c. Find P(X > 2|X > 1).

Problem 16 A company makes a certain device. We are interested in the lifetime of the device. It is estimated that around 2% of the devices are defective from the start so they have a lifetime of 0 years. If a device is not defective, then the lifetime of the device is exponentially distributed with a parameter A = 2 years. Let X be the lifetime of a randomly chosen device. a. Find the generalized PDF of X. b. Find P(X > 1). c. Find P(X > 2|X > 1).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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### Problem 16 A company makes a certain device. We are interested in the lifetime of the device. It is estimated that around 2% of the devices are defective from the start so they have a lifetime of 0 years. If a device is not defective, then the lifetime of the device is exponentially distributed with a parameter \(\lambda = 2\) years. Let \(X\) be the lifetime of a randomly chosen device. #### Questions: a. Find the generalized PDF of \(X\). b. Find \(P(X \geq 1)\). c. Find \(P(X > 2 \mid X \geq 1)\). d. Find \(E(X)\) and \(Var(X)\).
Transcribed Image Text:### Problem 16 A company makes a certain device. We are interested in the lifetime of the device. It is estimated that around 2% of the devices are defective from the start so they have a lifetime of 0 years. If a device is not defective, then the lifetime of the device is exponentially distributed with a parameter \(\lambda = 2\) years. Let \(X\) be the lifetime of a randomly chosen device. #### Questions: a. Find the generalized PDF of \(X\). b. Find \(P(X \geq 1)\). c. Find \(P(X > 2 \mid X \geq 1)\). d. Find \(E(X)\) and \(Var(X)\).
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