Question: A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteries-battery 1, battery 2, ..., battery

A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteries-battery 1, battery 2, ..., battery n. Initially, battery 1 and 2 are installed. Whenever a battery fails, it is immediately replaced by the lowest numbered functional battery that has not yet been put in use. Suppose that the lifetimes of the different batteries are independent exponential random variables each having rate . At a random time, call it T, a battery will fail and our stockpile will be empty. At that moment exactly one of the batteries-which we call battery X-will not yet have failed.

(a) What is P(X = n]?

(b) What is P(X = 1]?

(c) What is P(X = i]?

(d) Find E[T].

(e) What is the distribution of T?

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 Introduction To Probability Statistics Questions!

A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteriesbattery 1, battery 2,..., battery n. Initially, battery 1 and 2 are installed....

*17. A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of functional batteriesbattery 1, battery 2, battery n. Initially, battery 1 and 2 are installed....

23. A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteriesbattery 1, battery 2, . . . , battery n. Initially, battery 1 and 2 are...

*23. A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteriesbattery 1, battery 2 battery n. Initially, battery 1 and 2 are installed....

A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteriesbattery 1, battery 2, . . . , battery n. Initially, battery 1 and 2 are...

23. A flashlight needs two batteries to be operational. Consider such a flashlight along with a set of n functional batteriesbattery 1, battery 2,... , battery n. Initially, battery 1 and 2 are...

A spotlight needs two batteries to be operational. Consider such an electric lamp alongside a bunch of n practical batteriesbattery 1, battery 2, . battery n. At first, battery 1 and 2 are...

Write a technical description for the Brita Stainless Steel Water Bottle with Filter, 20 Ounce Premium Double Insulated Water Bottle, BPA Free, Carbon. This description should include the following...

What are the current strategic alternatives and recommended strategies? how would you make them work and make sure they're effective? ASE 6 A123 Systems: A New Lithium-Ion Battery System for Electric...

Apply the Estimation Theorem (i.e. Theorem 7.5 proved in Lecture 15) to obtain the following upper bounds: TT 1 | dz| (1) 1 (5;1) 22 8' eiz V -dz

Using the monthly data in VOLAT.RAW, the following model was estimated: where pcip is the percentage change in monthly industrial production, at an annualized rate, and pcsp is the percentage change...

Which of the following is not a standard of 3 G ? Question 1 7 options: TD - SCDMA GPRS UMTS CDMA 2 0 0 0

The lack of innovation and entrepreneurial focus at American Express (AmEx) may be because of hubris, inertia, and a lack of capability. The firms performance in 2014 was not, by any means, what...

Let r(p) be the reliability function. Show that r(p) = pir(1i ,p)+ (1 pi)r(0i ,p)

Compute the reliability function of the bridge system (see Fig. 9.11) by conditioning upon whether or not component 3 is working.

Compute upper and lower bounds of the reliability function (using Method 2) for the systems given in Exercise 4, and compare them with the exact values when pi 1 2 .

9 Fill in the missing amounts in each of the eight case situations below. Each case is independent of the others (Hint: One way to find the missing amounts would be to prepare a contribution format...

Sales promotions At the bottom of all its February sales receipts, Seifert Stores Inc. printed $2-off coupons. The coupons may be redeemed March 1-April 30. Seifert Stores Inc. accepts only cash,...

Oriole Corporation has the following account balances at December 31, 2025. Common stock, $5 par value $459,000 Treasury stock Retained earnings 95,000 2,451,000 Paid-in capital in excess of...