2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of...
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.
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.
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(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 = x ~ Bin(x,p)....
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.
(f) Find the conditional pmf of X given Z. Identify this
conditional distribution as a distribution known in class, and
give
the explicit parameters for the known distribution.
(g) Find the conditional expectation of X given Z.
2. (Lec 13 &15 & 16 pairs of discrete R.V., conditional pmf and conditional moments, 17 pts) We are studying the flow of packets at a switch, which receives packets from two transmission paths, during a given period of time. Let X and...
13. Let X and Y be rv's whose joint PMF is given by: Y=1 2 3 X=0 0.2 0.1 0 1 0.1 0.3 0. 2 . 0 0 0.3 Compute the covariance and correlation matrix of the random vector (X,Y).
Let X and Y be independent exponentially distribution
random variables with rate α and β respectively. Find P (X > Y
).
Question 13: Let X and Y be independent exponentially distribution random variables with rate a and B respectively. Find P(X> Y).
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
) Let Y ∼ Exp(λ). Given that Y = m, let X ∼ Pois(m).
Find the mean and
variance of X.
estrbetrecoralcional stribution. 2. (Anderson, 10, 11) Let Y ~ Exp(A). Given that Y = m, let X ~ Pois(m). Find the mean and variance of X 3 (Anderson 10