Question

Let {N1(t), t ≥ 0} and {N2(t), t ≥ 0} be two independent Poisson processes with...

Let {N1(t), t ≥ 0} and {N2(t), t ≥ 0} be two independent Poisson processes with rates λ1 and λ2, respectively. Define N(t) = N1(t) + N2(t). Use the definition to prove that {N(t), t ≥ 0} is a Poisson process with rate λ = λ1 + λ2.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

please rate me high.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose...
Let X1, X2,... be a sequence of independent random variables distributed exponentially with mean 1. Suppose that N is a random variable, independent of the Xi-s, that has a Poisson distribution with mean λ > 0. What is the expected value of X1 + X2 +···+ XN2? (A) N2 (B) λ + λ2 (C) λ2 (D) 1/λ2
Let X1 and X2 be independent Poisson random variables with respective parameters λ1 and λ2. Find...
Let X1 and X2 be independent Poisson random variables with respective parameters λ1 and λ2. Find the conditional probability mass function P(X1 = k | X1 + X2 = n).
Topic: Stochastic processes and poisson processes Let W1,W2, ... be the event times in a Poisson...
Topic: Stochastic processes and poisson processes Let W1,W2, ... be the event times in a Poisson process {X(t); t > 0} of rate 2. Suppose it is known that X(1) = n. For k<n, what is the conditional density function of W1,....Wk-1,.....,Wn given that Wk=w Please follow the comments and do the review before you do this question
Let X ∼ Poisson(µ1) and Y ∼ Poisson(µ2) be two independent random variables. Define Z =...
Let X ∼ Poisson(µ1) and Y ∼ Poisson(µ2) be two independent random variables. Define Z = X +Y . Show that X | Z = n ∼ Binomial( n, µ1 / (µ1 + µ2))
Two people enter the elevator in a 5-floor building. Let N1 and N2 denote the floors...
Two people enter the elevator in a 5-floor building. Let N1 and N2 denote the floors that they want to go to. Assume that N1 and N2 are independent and equtl to 2, 3, 4 and 5 with probabilities 1/4 each. (a) Write down the joint PMF (b) Calculate P(N1 > N2) and P(N1 = N2) (c) Let X1 and X2 denotethenumberofstopsthateachofthemwillmakebeforearriving to their floor. What is the support of X1 and X2? (d) Find the marginal PMF-s and the...
Consider a Poisson process with rate λ and let L be the time of the last...
Consider a Poisson process with rate λ and let L be the time of the last arrival in the interval [0, t], with L = 0 if there was no arrival. (a) Compute E(t − L). (b) What happens when we let t → ∞ in the answer to (a)?
Independent random variables X and Y follow binomial distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y....
Independent random variables X and Y follow binomial distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y. What will be the distribution of Z? Hint: Use moment generating function.
Let T  = z/(sqrt(w/v)) has a t-distribution with ν df, when Z ~ N(0, 1) is independent...
Let T  = z/(sqrt(w/v)) has a t-distribution with ν df, when Z ~ N(0, 1) is independent of W ~ χ2(ν);  Prove that V(T) = v/v-2 if ν > 2, Use that V(T) = E(T2) - µ2.
Consider a homogeneous Poisson process {N(t), t ≥ 0} with rate α. Now color each point...
Consider a homogeneous Poisson process {N(t), t ≥ 0} with rate α. Now color each point blue with probability p and red with probability q = 1 − p. Colors of distinct points are independent. Let X be the location of the second blue point that comes after the third red point. (That is after the location of the third red point, start counting blue points; the second one is X.) Find E(X).
Assume that arrivals come from two independent Poisson processes of males and females with respective rates...
Assume that arrivals come from two independent Poisson processes of males and females with respective rates of λ=4/hr and µ=6/hr. If the system is currently empty, find the probability that (a) there will be no arrivals in the next 10 minutes; (b) there will be no arrivals in the next 10 minutes, given the last arrival was over 9 minutes ago; (c) there will be no males arriving in the next 10 minutes, but at least one female; (d) a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT