probability
posted by JuanPro .
Consider a Poisson process with rate λ. Let N be the number of arrivals in (0,t] and M be the number of arrivals in (0,t+s], where t>0,s≥0.
In each part below, your answers will be algebraic expressions in terms of λ,t,s,m and/or n. Enter 'lambda' for λ and use 'exp()' for exponentials. Do not use 'fac()' or '!' for factorials. Follow standard notation.
For 0≤n≤m, the conditional PMF pM∣N(m∣n) of M given N is of the form ab! for suitable algebraic expressions in place of a and b.
a= unanswered
b= unanswered
For 0≤n≤m, the joint PMF pN,M(n,m) of N and M is of the form cn!d! for suitable algebraic expressions in place of c and d.
c= unanswered
d= unanswered
For 0≤n≤m, the conditional PMF pNM(nm) of N given M is of the form f⋅g!n!h! for suitable algebraic expressions in place of f, g, and h.
f= unanswered
g= unanswered
h= unanswered
E[NM]= unanswered

probability 
Mary
a = (lambda*s)^(mn)*e^(lambda*s)
b = mn
c = lambda^m*s^(mn)*t^n*e^(lambda*(s+t))
d = mn
f = (s^(mn)*t^n)/((s+t)^m)
g = m
h = mn
E[NM] = (lambda*t)*(lambda*s)+lambda*t+(lambda*t)^2
ALL CORRECT!!!
Respond to this Question
Similar Questions

math
THE MAXIMUM NUMBER OF CUSTOMERS ARRIVING DURING RANDOMLY CHOSEN 10MIN INTERVALS IS 5 AT A DRIVEIN FACILITY SPECIALIZING IN PHOTO DEVELOPMENT AND FILM SALES. IT HAS BEEN FOUND THE NUMBER OF ACTUAL SALES MADE FOLLOWS THE PROBABILITY … 
stat
Problem 2. THE PROBABILITY THAT A RANDOMLY CHOSEN SALES PROSPECT WILL MAKE A PURCHASE IS 0.20. IF A SALESMAN CALLS ON SIX PROSPECTS, A. WHAT IS THE PROBABILITY THAT HE WILL MAKE EXACTLY FOUR SALES? 
Business Stats
A busy restaurant determined that between 6:30 P.M. and 9:00 P.M. on Friday nights, the arrivals of customers are Poisson distributed with an average arrival rate of 4.32 per minute. What is the probability that at least 1 minute will … 
probability
In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for λ and 'mu' for μ. Follow standard notation. Shuttles bound for Boston depart from New York every hour on the hour (e.g., at exactly … 
probability
All ships travel at the same speed through a wide canal. Each ship takes t days to traverse the length of the canal. Eastbound ships (i.e., ships traveling east) arrive as a Poisson process with an arrival rate of λE ships per … 
probability
lengths of the different pieces are independent, and the length of each piece is distributed according to the same PDF fX(x). Let R be the length of the piece that includes the dot. Determine the expected value of R in each of the … 
Probability
In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for and 'mu' for . Follow standard notation. 1. Shuttles bound for Boston depart from New York every hour on the hour (e.g., at exactly one o'clock, … 
Probability
In parts 1, 3, 4, and 5 below, your answers will be algebraic expressions. Enter 'lambda' for λ and 'mu' for μ. Follow standard notation. Shuttles bound for Boston depart from New York every hour on the hour (e.g., at exactly … 
Probability
All ships travel at the same speed through a wide canal. Each ship takes t days to traverse the length of the canal. Eastbound ships (i.e., ships traveling east) arrive as a Poisson process with an arrival rate of λE ships per … 
Probability
Consider a Poisson process with rate λ. Let N be the number of arrivals in (0,t] and M be the number of arrivals in (0,t+s], where t>0,s≥0. In each part below, your answers will be algebraic expressions in terms of λ,t,s,m …