Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential n! distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula (): = k!(n - k)! (a) What is the probability that all thirteen bulbs fail before time t? (b) What is the probability that exactly k of the thirteen bulbs fail before time t? (c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that is exponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs fail before time t?

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...
icon
Related questions
Question
Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential
n!
distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula ():
=
k!(n - k)!
(a) What is the probability that all thirteen bulbs fail before time t?
(b) What is the probability that exactly k of the thirteen bulbs fail before time t?
(c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that is
exponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs fail
before time t?
Transcribed Image Text:Suppose that you have thirteen lightbulbs, that the lifetime of each is independent of all the other lifetimes, and that each lifetime has an exponential n! distribution with parameter A. (Do not enter combinations as (). Enter combinations using the formula (): = k!(n - k)! (a) What is the probability that all thirteen bulbs fail before time t? (b) What is the probability that exactly k of the thirteen bulbs fail before time t? (c) Suppose that twelve of the bulbs have lifetimes that are exponentially distributed with parameter 1 and that the remaining bulb has a lifetime that is exponentially distributed with parameter 8 (it is made by another manufacturer). What is the probability that exactly seven of the thirteen bulbs fail before time t?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON