15 Let X and Y have a trinomial distribution with n = 8, P1 = 0.4...
Suppose (X,Y) follows a trinomial distribution (5, 1/3, 1/4). a. Find E(X) b. Find E(Y) c. Find Var(X) d. Find Var(Y) e. Find Cov (X,Y) f. Find p (correlation coefficient)
Let the two-dimensional random variable (X, Y) have the joint density fx.r(x, y) = 16 - x - y)I(0, 2)(x)/(2,4,(y). (a) Find &[Y| X = x]. (6) Find &[Y|X = x]. © Find var (Y|X=x]. (d) Show that &[Y] = { [E[Y|X]]. (e) Find &[XY|X=x]. Tinomial distribution (multinomial with k + 1 =3) of two random variables The trinomial distribution (mu X and Y is given by fx.x(x, y) = x!y!(n - x - y)!' for x, y=0, 1, ...,...
Let X and Y have the following joint distribution X/Y 0 1 0 0.4 0.1 1 0.1 0.1 2 0.1 0.2 a) Find Cov(4+2X, 3-2Y) b) Let Z = 3X-2Y+2 Find E[Z] and σ 2Z c) Calculate the correlation coefficient between X and Y. What does this suggest about the relationship between X and Y? d) Show that for two nonzero constants a and b Cov(X+a, Y+b) = Cov(X,Y)
Any help would be appreciated! Problem 4 Let (X, Y)~ N and Z = X1(XY > 0}-X1(XY < 0} (1) Find the distribution of Z (2) Show that the joint distribution of Y and Z is not bivariate normal.
2. Let the pair (X,Y) have joint PDF fxy(x, y) = c, with 2.2 + y2 <1. (a) Find c and the marginal PDFs of X and Y. (b) What are the means of X and Y ? No calculations are needed, only a brief expla- nation is required. (c) Find the conditional PDF of Y given X = x and deduce E|Y|X = x]. (d) Obtain E(XY) and compare it to E[X]E[Y). (e) Are X and Y independent? Explain....
1. Let X ~ Bin(n = 12, p = 0.4) and Y Bin(n = 12, p = 0.6), and suppose that X and Y are independent. Answer the following True/False questions. (a) E[X] + E[Y] = 12. (b) Var(X) = Var(Y). (c) P(X<3) + P(Y < 8) = 1. (d) P(X < 6) + P(Y < 6) = 1. (e) Cov(X,Y) = 0.
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer. (20 points) Consider the following joint distribution of X and...
Let X ~ N(0, 1) and let Y be a random variable such that E[Y|X=x] = ax +b and Var[Y|X =x] = 1 a) compute E[Y] b) compute Var[Y] c) Find E[XY]
Let X and Y have a bivariate normal distribution with parameters μX = 10, σ2 X = 9, μY = 15, σ2 Y = 16, and ρ = 0. Find (a) P(13.6 < Y < 17.2). (b) E(Y | x). (c) Var(Y | x). (d) P(13.6 < Y < 17.2 | X = 9.1). 4.5-8. Let X and Y have a bivariate normal distribution with parameters Ax-10, σ(-9, Ily-15, σǐ_ 16, and ρ O. Find (a) P(13.6< Y < 17.2)...
Let X and Y have the following joint distribution: X/Y -1 1 0 0.2 0.15 2 0.1 0.2 4 0.25 0.1 a) Find the probability distributions for X and Y b) Find E[X] and E[Y] c) Find the probability that X is larger than 1 d) Find E[XY]