Question: The exponential distribution is the only continuous distribution to have the memoryless property (we showed this in terms of the geometric distribution). a. Prove ????(????>????+????|????>????)=????(????>????)

The exponential distribution is the only continuous distribution to have the memoryless property (we showed this in terms of the geometric distribution).

a. Prove ????(????>????+????|????>????)=????(????>????)

b. Whenever you purchase a lightbulb, the package will display the mean lifetime. It turns out that such lifetimes are exponentially distributed. For a 60-watt incandescent light bulb, the average lifetime was 1200 hours. Given that the bulb has worked for more than 1500 hours, find the probability that it will work for more than 1800 hours. (Use the memoryless property.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The exponential distribution is the only continuous distribution to have the memoryless property (we showed this in terms of the geometric distribution). Whenever you purchase a lightbulb, the...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

\fCHAPTER 14 Server Farms: M/M/k and M/M/k/k In today's high-volume world, almost no websites, compute centers, or call centers consist of just a single server. Instead a \"server farm\" is used. The...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

i know how to do the first prat for question 7. But i do not know how to deal with the second part. Also, the proof of question 8 is hard for me as well. 7. Prove the "memoryless property" of...

Stock redemption is generally treated as an exchange, in which the stockholders give up their stock in exchange for cash or property. However, the Internal Revenue Code (IRC) does provide...

Describe, in outline, each of the implicit surface, NURBS surface, and constructive solid geometry methods for defining three-dimensional shapes. (b) Compare and contrast the three methods. (a)...

Suppose that the random variable X has an exponential distribution with parameter ? > 0. (i) What are the probability density function, fX(x), and the probability distribution function, FX(x), for...

Financial markets are characterized by volatility, which is linked to the standard deviation of returns. One interesting feature of volatility is that we observe periods of relative calm, in which...

Graph the systems of inequalities in Problems. Introduce slack variables to convert each system of inequalities to a system of equations, and find the basic solution of the system. Construct a table...

Explain what are biofuels? Which are the main crops used to produce biofuels? What are 1st, 2nd, 3rd and 4th generation biofuels? (essay format)

Stocks have historically earned about 6 . 6 % per year in real terms ( i . e . , adjusting for inflation ) , while government bonds have earned about 3 . 6 % per year. A $ 1 , 0 0 0 investment in...

2023 1040 form 1.Phillip and Claire are married and file a joint return. Phillip is self-employed as a real estate agent, and Claire is a flight attendant. Phillip and Claire have three dependent...