Calculate the average time that the process spends

Assignment Help Basic Statistics

Reference no: EM131131053

We consider a system composed of three components placed in parallel and operating independently. The lifetime X_i(in months) of component I has an exponential distribution with parameter A, for i = 1,2,3. When the system breaks down, the three components are replaced in an exponential time (in months) with parameter μ. Let X(t) be the number of components functioning at time t. Then {X(t),t > 0} is a continuous-time Markov chain whose state space is the set {0,1,2,3}.

(a) Calculate the average time that the process spends in each state.

(b) Is the process {X(t),t ≥ 0} a birth and death process? Justify.

(d) Calculate the limiting probabilities of the process if λ = μ.

Reference no: EM131131053

Questions Cloud

Explain the advantages and disadvantages of the partnership : Brent Houghton and Dick Kreibach are considering a business venture. They ask you to explain the advantages and disadvantages of the partnership form of organization.

Number of individuals in the population to be equal : (a) Let Tn := min{t > 0: X{t) = n (> 1)}. That is, Tn is the time needed for the number of individuals in the population to be equal to n. Show that the probability density function of Tn is given by

Number of individuals in the system at a time instant : (a) Calculate, assuming that λ = μ, the average number of individuals in the system at a time instant t (large enough), given that the system is not empty at this time.

Select the right option for the given problem : Unless he ____ hard, he'll fail the exams. When he ____ finished the exam, he'll speak to you

Calculate the average time that the process spends : We consider a system composed of three components placed in parallel and operating independently. The lifetime Xi(in months) of component I has an exponential distribution with parameter A, for i = 1,2,3.

The following probability density function : Let {N(t),t > 0} be a counting process such that N(0) = 0. When the process is in state J, the next state visited will be j + 1, for all j ≥ 0. Moreover, the time τj that the process spends in state j has the following probability density function

Expain the relevant costs for the expansion decision : From the scenario for Katrina's Candies, determine the relevant costs for the expansion decision, and distinguish between the short run and the long run costs.

Write an essay on relationships and teen pregnancy issues : Write an essay of 6 pages on the following topic:- Relationships and Teen Pregnancy Issues

An exponential distribution with mean equal : We consider the particular case of the gambler's ruin problem for which fc = 4 and p = 1/2. Suppose that the length T (in minutes) of a play (the outcome of which is the player's winning or losing $1) has an exponential distribution with me..

User Account

All Pages