help plz 2. (Anderson, 10.11) Let Y ~Exp(A). Given that Ym, let X ~Pois(m). Find the...
) 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
Suppose X~Pois(λ1) and Y~Pois(λ2). Find the conditional mass function for X given X+Y = m
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)....
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.
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(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.
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.
Question 4 16 marks Let Y N(Hy, o). Then X := exp(Y) is said to be lognormally distributed with p.d.f. (In(x)-Hy) exp 202 fx(x) TOYV27 and denoted as LN(Hy, of). Let Xı,... , X, be random samples from the LN(Hy,of) distribution (a) Find the maximum likelihood estimator for ty, which we denote as fty (Hint: Use the fact that Yi In(X) is normally distributed with known mean and variance) Verify that the sought stationary point is a maximum (b) Verify...
4) Suppose that Y~exp(8). Let X = ln(Y). Find the pdf of X. 5) Let Y and Y2 be iid U(0,1). Let S YY2. Find the pdf of S.
Let X and Y be independent random variables with X = N(0, 1) and Y = Exp(1). Find E( |X| (Y + 1)^2 ).