Mathematical Statistics Question Example 80. A system consists of five identical components connected in series as shown:3 4H3-As soon as one component fails, the entire system will fail. Suppose each component has alifetime that is exponentially distributed with 2 = .01 and that components fail independently ofone another. Define events A; = {ith component lasts at least t hours}, i= 1, ..., 5, so that the A,s%3Dare independent events. Let X = the time at which the system fails-that is, the shortest(minimum) lifetime among the five components.(a) The event {X >t} is equivalent to what event involving A1, ..., A5?(b) Using the independence of the five A,s, compute P(X > t). Then obtain F(t) = P(X < t) andthe pdf of X. What type of distribution does X have?(C) Suppose there are n components, each having exponential lifetime with parameter 2. Whattype of distribution does X have?Croccing Behaviors and Safety at

Solution : Given : Series system of 5 components and lifetime of components have exponential…

A system consists of fivé idêntičal components connected in series as shown: H2 4 As soon as one component fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with 2= .01 and that components fail independently of one another. Define events A; = {ith component lasts at least t hours}, i= 1, ..., 5, so that the A,s the time at which the system fails-that is, the shortest are independent events. Let X (minimum) lifetime among the five components. (a) The event {X > t} is equivalent to what event involving A1, .. ., A5? (b) Using the independence of the five A,s, compute P(X > t). Then obtain F(t) = P(X < t) and the pdf of X. What type of distribution does X have? (c) Suppose there are n components, each having exponential lifetime with parameter 2. What tyne of distribution does X have? !! nd Safety at

A system consists of fivé idêntičal components connected in series as shown: H2 4 As soon as one component fails, the entire system will fail. Suppose each component has a lifetime that is exponentially distributed with 2= .01 and that components fail independently of one another. Define events A; = {ith component lasts at least t hours}, i= 1, ..., 5, so that the A,s the time at which the system fails-that is, the shortest are independent events. Let X (minimum) lifetime among the five components. (a) The event {X > t} is equivalent to what event involving A1, .. ., A5? (b) Using the independence of the five A,s, compute P(X > t). Then obtain F(t) = P(X < t) and the pdf of X. What type of distribution does X have? (c) Suppose there are n components, each having exponential lifetime with parameter 2. What tyne of distribution does X have? !! nd Safety at

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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