Question: Consider a system containing n components, where the lifetimes of the components are independent random variables and each has pdf fY(y) = ey, y >

Consider a system containing n components, where the lifetimes of the components are independent random variables and each has pdf fY(y) = λe−λy, y > 0. Show that the average time elapsing before the first component failure occurs is 1/nλ.

Step by Step Solution

★★★★★

3.49 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Using the solution to Question 3106 ... 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)

681-M-C-M-S (414).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Show that, if X1,..., Xn are independent random variables, and a1,..., an are constants, then Var(a X1 + + an Xn) = af Var(X1) ++a, Var(Xn).

Suppose that a point (X, Y) is to be chosen at random in the xy-plane, where X and Y are independent random variables and each has the standard normal distribution. If a circle is drawn in the...

Suppose that a point (X, Y, Z) is to be chosen at random in three-dimensional space, where X, Y, and Z are independent random variables and each has the standard normal distribution. What is the...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

1 1. Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected, and the alcohol content of each bottle is determined. Let denote the average alcohol content for the...

Questions . Please answer each question in detail 1) Consider the following technology: c(yi) = yi2 +2yi +4. Many firms have access to this technology, in fact so many that there is not room for all...

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...

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...

solve these practice problems Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.65 and standard deviation .85 (suggested in...

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...

An off-market forward contract is a forward where either you have to pay a premium or you receive a premium for entering into the contract. (With a standard forward contract, the premium is zero.)...

What do the relational features restrict, project, and join mean?

12. A building that was purchased December 31, 2001, for 2,500,000 was originally estimated to have a life of 50 years with no residual value at the end of that time. Depreciation has been recorded...

Direct versus Indirect Method For each of the following items, indicate whether it would appear on a statement of cash fl ows prepared using the direct method (D) or the indirect method (I). ______...

Determine whether each of these pairs of sets are equal. a) {1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) , {}

For each of the following sets, determine whether 2 is an element of that set. a) {x R | x is an integer greater than 1} b) {x R | x is the square of an integer} c) {2, {2}} d) {{2}, {{2}}} e)...

Determine whether each of these statements is true or false. a) 0 b) {0} c) {0} d) {0} e) {0} {0} f) {0} {0} g) {} {}

It has been determined that, in aggregate, financial institutions with depository accounts currently hold excess reserves equal to $3 billionthat is, they hold $3 billion more than is necessary to...

You are choosing between two projects. The cash flows for the projects are given in the following table ( $ million): a. What are the IRRs of the two projects? b. If your discount rate is 4.7%, what...

You are thinking of purchasing a house. The house costs S350,000. You have S50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The...