8. We say that two discrete random variables X and Y , are independent when P(X...
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 K = X + Y
Let X and Y be two discrete random independent random variables. p(x) = 1/3 for x =-2,-1,0 p(y) = 1/2 for y =1,6 Z = X + Y. What is the distribution of Z using the method of MGF's
2. Let X and Y be two independent discrete random variables with the probability mass functions PX- = i) = (e-1)e-i and P(Y = j-11' for i,j = 1, 2, Let {Uni2 1} of i.i.d. uniform random variables on [0, 1]. Assume the sequence {U i independent of X and Y. Define M-max(UhUn Ud. Find the distribution
Problem D: Suppose X1, .,X, are independent random variables. Let Y be their sum, that is Y 1Xi Find/prove the mgf of Y and find E(Y), Var(Y), and P (8 Y 9) if a) X1,.,X4 are Poisson random variables with means 5, 1,4, and 2, respectively. b) [separately from part a)] X,., X4 are Geometric random variables with p 3/4. i=1
X1 and X2 are discrete random variables (and are independent) with probability functions: p1(x1) = 1/3 for x1 = −2 ,−1 , 0 p2(x2) = 1/2 for x2 = 1, 6 Let Y = X1 + X2 a). Find the MGF of X1, X2 and Y b). USE MGFS derived in part a) to determine the probability mass function of Y. Note: MGFs in part a) must be used to determine the pmf of Y in part b)
number2 how to solve it? Are x1 and x2 independent - yes, they are independent. Random variables X and Y having the joint density 1. 8 2)u(y 1)xy2 exp(4 2xy) fxy (x, y) ux- _ 3 1 1 Undergo a transformation T: 1 to generate new random variables Y -1. and Y2. Find the joint density of Y and Y2 X3)1/2 when X1 and X2 (XR 2. Determine the density of Y are joint Gaussian random variables with zero means...
Random variables X and Y are independent. the random variable X has density p(x) and Y is a discrete random variable having just two values: 1 with probability 1/3 and 2 with probability 2/3. Calculate the density of Z=X+Y.
Let X1, X2, X3 be independent random variables with E(X1) = 1, E(X2) = 2 and E(X3) = 3. Let Y = 3X1 − 2X2 + X3. Find E(Y ), Var(Y ) in the following examples. X1, X2, X3 are Poisson. [Recall that the variance of Poisson(λ) is λ.] X1, X2, X3 are normal, with respective variances σ12 = 1, σ2 = 3, σ32 = 5. Find P(0 ≤ Y ≤ 5). [Recall that any linear combination of independent normal...
L.11) Sums of independent random variables a) If X1 , X2 X, , , Xn are independent random variables all with Exponential μ distribution, then what is the distribution of XII + 2 +X3 + .tX b) If X is a random variable with Exponential[u] distribution, then what is the distribution of x +X1? c) If X1 , X2 , Х, , , X are independent random variables all with Normal 0. I distribution, then what is the distribution of...
Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set {1, 3} and Y has a discrete uniform distribution over the set {1, 2, 3}. Let V = X + Y and W = X − Y . (a) Find the PMFs for V and W. (b) Find mV and (c) Find E[V |W >0].