Suppose that five components are functioning simultaneously, that the lifetimes of the components are i i d , and that each lifetime has the exponential distribution with parameter Let T1 denote the time from the beginning of the process until one of the components fails and let T5 denote the total time until all five components have failed Evaluate Cov(T1, T5)

Question: Suppose that five components are functioning simultaneously, that the lifetimes of the components are i.i.d., and that each lifetime has the exponential distribution with parameter

Suppose that five components are functioning simultaneously, that the lifetimes of the components are i.i.d., and that each lifetime has the exponential with parameter β. Let T1 denote the time from the beginning of the process until one of the components fails; and let T5 denote the total time until all five components have failed. Evaluate Cov(T1, T5).

Step by Step Solution

★★★★★

3.33 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We can express T5 as T1 V where V is the time required after one of the co... 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)

602-M-S-D-D (774).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose X has an exponential distribution with mean equal to 10.Determine following: (a) P(X > 10) (b) P(X > 20) (c) P(X > 30)

Suppose that n items are being tested simultaneously, the items are independent, and the length of life of each item has the exponential distribution with parameter . Determine the expected length of...

Suppose that the random variables X1, . . . , Xk are independent and Xi has the exponential distribution with parameter i (i = 1, . . . , k). Let Y = min{X1, . . . , Xk}. Show that Y has 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)....

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

A system consists of five identical components connected in series as shown: As soon as one components fails, the entire system will fail. Suppose each component has a lifetime that is exponentially...

please do both questions and details all steps ! please make it easy to follow Question \#1: Consider a system consisting of three components as pictured. The system will continue to function as long...

) Explain the collision detection mechanism applied in standard wired medium access control associated with CSMA and indicate why this might be unsuitable for wireless networks. [2 marks] (ii)...

) Consider integer division of one two's-complement binary number by another. Programming languages may vary in the result when one argument is negative. What differing conventions might they be...

Consider a system consisting of three components as pictured. The system will continue to function as long as the f(x, y) 5 e xe2x(11y) x $ 0 and y $ 0 0 otherwise g m k50 a m k bak bm2k 5 (a 1 b)m...

In this experiment, you will be performing an elimination reaction on 2-butanol (shown below). What is the elimination mechanism (E1 or E2)? Give a short explanation. OH HSO4 Heat

What do advocates claim about the influence of spirituality on the performance of employees?

Problem 7 - 3 Call Premium ( LG 7 - 1 ) A 6 . 6 percent corporate coupon bond is callable in five years for a call premium of one year of coupon payments. Assuming a par value of $ 1 , 0 0 0 , what...

20. Sora Industries has 60 million outstanding shares, $120 million in debt, $40 million in cash, and the following projected free cash flow for the next four years: a. Suppose Soras revenue and free...

The article "On Assessing the Accuracy of Offshore Wind Turbine Reliability Based Design Loads from the Environmental Contour Method" (Intl. J. of Offshore and Polar Engr., 2005: 132-140) proposes...

Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that...

In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B =...

Suppose the following two independent Investment opportunities are available to Fitz, Inc. The appropriate discount rate is 10 percent Year 0 1 Project Alpha -$3.900 2.000 1.900 1,300 Project Beta...

A company has a 13% WACC and is considering two mutually exclusive investments (that cannot be repeated) with the following cash flows: 0 1 2 3 4 5 6 7 Project A -$300 -$387 -$193 -$100 $600 $600...

1 point A currently used machine costs $ 5 , 0 0 0 annually to run. What is the maximum that should be paid to replace the machine with one that will last 4 years and will cost only $ 2 , 5 0 0...