Homework Help is Here – Start Your Trial Now!
Math
Statistics
3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours) by random variable X and Y, each having exponential distribution with parameter A equal to 0.2 and 0.9 respectively. Assume that X and Y are independent of each other. (a) What is the joint pdf of X and Y? (b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to calculate P(X ≤ 1, Y ≤ 1)? (c) What is the probability that Bulb B lasts more than twice as long as Bulb A? (d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours? (e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours?

3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours) by random variable X and Y, each having exponential distribution with parameter A equal to 0.2 and 0.9 respectively. Assume that X and Y are independent of each other. (a) What is the joint pdf of X and Y? (b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to calculate P(X ≤ 1, Y ≤ 1)? (c) What is the probability that Bulb B lasts more than twice as long as Bulb A? (d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours? (e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
See similar textbooks
icon
Related questions
Question
3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours) by random variable X and Y, each having exponential distribution with parameter A equal to 0.2 and 0.9 respectively. Assume that X and Y are independent of each other. (a) What is the joint pdf of X and Y? (b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to calculate P(X ≤ 1, Y ≤ 1)? (c) What is the probability that Bulb B lasts more than twice as long as Bulb A? (d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours? (e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours?
Transcribed Image Text:3. Suppose the lifetimes of two light bulbs (Bulb A and Bulb B) are measured (in 1000 hours) by random variable X and Y, each having exponential distribution with parameter A equal to 0.2 and 0.9 respectively. Assume that X and Y are independent of each other. (a) What is the joint pdf of X and Y? (b) What is the probability that each light bulb lasts at most 1000 hours (Hint: You want to calculate P(X ≤ 1, Y ≤ 1)? (c) What is the probability that Bulb B lasts more than twice as long as Bulb A? (d) What is the probability that the total lifetime of the two bulbs is at most 2000 hours? (e) What is the probability that the total lifetime of the two bulbs is between 1000 and 2000 hours?
Expert Solution
steps

Step by step

Solved in 2 steps with 9 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
SEE MORE TEXTBOOKS