Number of customers in the system

Assignment Help Basic Statistics

Reference no: EM131005825

1. Consider an in?nite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. Let X(t) denote the number of customers in the system at time t. Find

(a) E[X(t + s)|X(s) = n];

(b) Var[X(t + s)|X(s) = n].

2. Suppose that people arrive at a bus stop in accordance with a Poisson process with rate λ. The bus departs at time t. Let X denote the total amount of waiting time of all those who get on the bus at time t. We want to determine Var(X). Let N(t) denote the number of arrivals by time t.

(a) What is E[X|N(t)]?

(b) Argue that Var[X|N(t)]= N(t)t2/12.

Reference no: EM131005825

Questions Cloud

Transition probabilities of markov chains : (a) If F is the exponential distribution with rate λ, which, if any, of the processes {Xn}, {Yn} is a Markov chain? (b) If G is the exponential distribution with rate μ, which, if any, of the processes {Xn}, {Yn} is a Markov chain? (c) Give the trans..

Find total expected return : (a) Find your total expected return. (b) Find the value of t that maximizes the total expected return.

Calculate the conditional distribution : Find the conditional distribution of T given that N = n. Calculate the conditional distribution of N, given that T = t, and notice that it is distributed as 1 plus a Poisson random variable with mean λ(1 - p)t.

Determining the poisson process with rate : Policyholders of a certain insurance company have accidents at times distributed according to a Poisson process with rate λ. The amount of time from when the accident occurs until a claim is made has distribution G.

Number of customers in the system : 1. Consider an in?nite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. Let X(t) denote the number of customers in the system at time t. F..

Identify the overarching goal for your practicum project : Identify the overarching goal for your Practicum Project. Consider how you can achieve your Practicum Project goal through the development and fulfillment of objectives

Billion interest payments on the national debt : Suppose the sum of consumption, investment, and government spending is $620 billion, where investment includes involuntary inventory accumulation of $2 billion in addition to expenditure on plant and equipment, and government spending includes $5 bil..

Distribution of the number of failures : What is the distribution of the number of failures by time t? What is the distribution of the number of ?aws that remain in the system at time t? Are the random variables in parts (a) and (b) dependent or independent?

Advantage of monetary policy over fiscal policy : What is the major advantage of monetary policy over fiscal policy? 1. monetary policy can be undertaken more quickly 2. monetary policy is more effective

User Account

All Pages