Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2), respectively.
(a) Find the distribution of Z = X + Y .
(b) Find the distribution of X|X + Y .
(c)If X∼Pois(λ1) and Y|X=x∼Bin(x,p). Find the distribution of Y.
Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2), respectively. (a) Find the...
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X X +Y. (c) If X Pois(11) and Y|X = r ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X +Y. (b) Find the distribution of X X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X +Y.. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(11) and Pois(2), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X+Y. (c) If X Pois (41) and Y|X = x~ Bin(x, p). Find the distribution of Y.
Suppose X~Pois(λ1) and Y~Pois(λ2). Find the conditional mass function for X given X+Y = m
Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ. Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ.
Let X, Y and Z be three independent Poisson random variable with parameters λι, λ2, and λ3, respectively. For y 0,1,2,t, calculate P(Y yX+Y+Z-t) (Hint: Determine first the probability distribution of T -X +Y + Z using the moment generating function method. Moment generating function for Poisson random variable is given in earlier lecture notes) Let X, Y and Z be three independent Poisson random variable with parameters λι, λ2, and λ3, respectively. For y 0,1,2,t, calculate P(Y yX+Y+Z-t) (Hint:...
7A,B,C Ar Y. Y, and : Let the joint d2 independent! Are they pairwise independent? obability distribution function of X,Y, and Z be given by Flz, y, z) = (1-e-Ai*)(1-e-wa-e-A3*), x, y, z > 0, where A1, λ2, λ3 > 0. (a) Are X, Y, and Z independent? Find the joint probability density function of X, Y, and Z. (b) (c) Find P(X <Y<Z).
1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively. 1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively.
1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively. 1) Find as an algebraic expression the mean life of a parallel system with two components, each of which has an exponential life distribution with hazard rate λ1 & λ2 respectively.