The poisson process over the entire real line

Reference no: EM131130636

Suppose that {N(t),t ≥ 0} is a Poisson process with rate λ > 0. For a fixed time instant t > 0, we consider the random variables A(t) and D(t)

(a) Calculate the distribution of both A(t) and D(t).

(b) What is the distribution of A(t) + D(t)?

(c) Suppose now that we consider the Poisson process over the entire real line, that is, {N(t),t ∈ R}. What then is the distribution of A(t) + D(t)?

(d) In (c), we can interpret the sum A(t) + D(t) as being the length of the interval, between two events, which contains the fixed time instant t. Explain why the distribution of this sum is not an exponential distribution with parameter λ.

Reference no: EM131130636

Questions Cloud

State of economy security return : Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. Assuming that all three states are equally likely. State of Economy Security Return If State Occurs Recession –6 % Normal 10 Boom..

A birth and death process with state space : Let {X(t), t ≥ 0} be a birth and death process with state space {0,1,2} and having the following birth and death rates: λo= λ1 = λ > 0, μ1 unknown, and μ2 = μ1 > 0. For what value(s) of μ1 is the process regenerative? Justify.

Why did you choose to participate in these activities : Are you involved in any civic engagements or volunteer activities in your community? Name them. Why did you choose to participate in these activities? OR Why haven't you become involved in community events and volunteer opportunities?

What is the nature and purpose of criminal law : What is the nature and purpose of criminal law? In your response, identify commonalities of purpose within law enforcement, corrections, the courts, and social services.

The poisson process over the entire real line : (c) Suppose now that we consider the Poisson process over the entire real line, that is, {N(t),t ∈ R}. What then is the distribution of A(t) + D(t)?

Calculate the arithmetic return and geometric return : You are given the returns for the following three stocks: Year Stock A Stock B Stock C 1 14 % 14 % −19 % 2 14 14 34 3 14 22 37 4 14 7 14 5 14 13 4 Calculate the arithmetic return, geometric return, and standard deviation for each stock.

Current articles about nafta at the library : Research some current articles about NAFTA at the library. Write an essay in which some of the current pros cons of this Agreement are discussed.

What are the opportunity costs of reducing expenditures : What are the opportunity costs of reducing expenditures (such as on education and social services programs), compared to the option of raising taxes? Why?

What is the project sales for next year : Gary’s Pipe and Steel company expects sales next year to be $700,000 if the economy is strong, $400,000 if the economy is steady, and $250,000 if the economy is weak. Gary believes there is a 20 percent probability the economy will be strong, a 50 pe..

User Account

All Pages