Question: You have two lightbulbs for a particular lamp. Let X = the lifetime of the first bulb and Y = the lifetime of the second

You have two lightbulbs for a particular lamp. Let X = the lifetime of the first bulb and Y = the lifetime of the second bulb (both in 1000s of hours). Suppose that X and Y are independent and that each has an exponential distribution with parameter λ = 1.
a. What is the joint pdf of X and Y?
b. What is the probability that each bulb lasts at most 1000 hours (i.e., X ≤ 1 and Y ≤ 1)?
c. What is the probability that the total lifetime of the two bulbs is at most 2? Draw a picture of the region A = {(x, y): x ≥ 0, y ≥ 0, x + y ≤ 2} before integrating.
d. What is the probability that the total lifetime is between 1 and 2?

Step by Step Solution

★★★★★

3.29 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b By independence PX 1 and Y 1 ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

1172-M-S-D-R-V(1156).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. The thickness of these layers is critical if specifications regarding the final...

The lifetimes of lightbulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 hours. The population distribution is normal. Suppose that you purchase...

Let X represent the error in making a measurement of a physical characteristic or property (e.g., the boiling point of a particular liquid). It is often reasonable to assume that E(X) = 0 and that X...

You have two lightbulbs for a particular lamp. Let X the lifetime of the first bulb and Y the lifetime of the second bulb (both in 1000s of hours). Suppose that X and Y are independent and that...

Can you give the answer for all of this questions with explanation, Please? Thank you so much! Question 1 : Question 4 : Suppose a particular manufacturing process for lightbulbs results in lifetimes...

solve the question HOW People Getl heir News The Brunswick Research Organization surveved 50 randomly,r selected individuals and asked them the pmal'f wag.r they received the daily news. Their...

I need help solving these problems. Please help me by answering and showing explanations. Question 3 1 pts When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear...

Only number 3 in the following picture: ._._._...._._.- _...._...,... -1 _-__. _. - Problem 3. Hypothesis test with a continuous observation 2/3 points (graded) Let 8 be a Bernoulli random variable...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Do this in jupyter notebook if possible or using python programming. 1) An airline runs a small commuter flight that has 10 seats. The probability that a passenger turns up for the flight is 0.92....

(i) What is the approximate annualized yield on a 6-month Treasury bill that is sold at 99 in the primary market? Show your calculations. (ii) A 10-year Treasury bond (TBOND1) is sold on the market...

18. The diagram shows two spheres of mass m suspended from wires of negligible mass. The length between the pivot points and the centres of each sphere is L. The two suspension points lie on a...

! Required Information Exerclse 5 - 9 ( Static ) Prepare a Profit Graph [ LO 5 - 8 ] [ The following information applles to the questions displayed below. ] Jaffre Enterprises distributes a single...

For the problem you have defined, develop an analytical model, research question, and the appropriate hypotheses. Discuss these with the decision maker you visited earlier.

A sample of 20 students who had recently taken introductory statistics yielded the following information on brand of calculator owned (T = Texas Instruments, H = Hewlett- Packard, C = Casio, S =...

Use the intuitive argument sketched in this section to obtain the general formula for the joint pdf of two order statistics given in the last proposition.

For a few years, the SAT consisted of three components: writing, critical reading, and mathematics. Let W = SAT Writing score and X = SAT Critical Reading score for a randomly selected student....

Ratios that help determine whether a company can access its cash and pay its debts that mature in less than a year are called (Liquidity; Market-Value or Market-based; Dividend Policy; Profitability;...

Lauryn's Doll Co. had EBIT last year of $42 million, which is net of a depreciation expense of $4.2 million. In addition, Lauryn's made $6 million in capital expenditures and increased net working...

Use the information in the table below, about the shares of BMO, to answer the next question: Asset Expected Standard Return Deviation Correlations Market BMO 1.00 ?? BMO Risk-Free Rate Market...