Stats please show the steps 10. Suppose we have a frequency function for two variables X...
Let the frequency function of the joint distribution of the random variables X and Y P(X = 2, Y = 3) = P(X = 1, Y = 2) = P(X = -1, Y = 1) = P(X = 0, Y = -1) = P(X = -1, Y = -2) = 3 a) Determine the marginal distributions of the random variables X and Y. b) Determine Cov(X,Y) and Corr(X,Y). c) Determine the conditional distributions of the random variable Y as a...
2. Suppose X and Y are continuous random variables with joint density function f(x, y) = 1x2 ye-xy for 1 < x < 2 and 0 < y < oo otherwise a. Calculate the (marginal) densities of X and Y. b. Calculate E[X] and E[Y]. c. Calculate Cov(X,Y).
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
5. Suppose we have two random variables X and Y. They are discrete and have the exact same distribution and also independent. You see below the distribution of X which of course also the distribution of Y as well, that is what we called independent and identically distributed) P(X =- X. Remem- a./ (-) Find and draw the cumulative distribution function F() function of ber that F(x) -P(X S) HINT: For the next 3 parts you might want to make...
please show steps to find the given answers. Problem 3 (40 pts) Two random variables X and Y are jointly distributed, based on the equation JXY (1, Y) |xy (,y) = } : (1,Y) E D 10 (, y) &D (1) where D is the region illustrated below. 1. Find k. Answer: k = } 2. Find expressions for, and sketch, the marginal distributions fx(x) and fy(y) Answer: plomba 0<<1 1<r < 2 2 < < Sy() – 24,2 y...
Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.a) What is f.d.p.c. of (X,Y). Calculate P(0 < X ≤ 1, Y > 1). Make a graphic sketch of the regionthat you used to calculate the probability. b) Determine the marginal distributions. (X, Y ) are independent?c) Find E[X] ,V AR[X], E[Y ] e V AR[Y ];d) Determine the conditional distributions. Use the conditionals to answer : (X, Y ) areindependent?e) Calculate E[XY ],...
Suppose X and Y are jointly continuous random variables with probability density function f(х+ у)={1/6(x + y), 0 < х < 1, 0 < у < 3; 0 , else} a) Find E[XY]. b) Are X and Y independent? Justify your answer citing an appropriate theorem.
please show steps, thank you (Sec. 5.2, 00) Suppose X and Y are independent random variables with E[X] = 6, E[Y ] = −3, Var[X] = 9, and Var[Y ] = 25. Find: (a) E[2Y − X] (b) Var[2Y − X] (c) Cov[X, Y ] (d) ρ[X, Y ] (e) Cov[5X + Y, Y ] (f) Cov[X, 2Y − X]
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
Q3. . Suppose that joint probability function of X and Y is given by | 1/7, z = 5, y = 0 Px,y(, ) 0, otherwise. a. Find the marginal distribution of X and Y b. Find E(X|y = 4] c. Compute Cov(X, Y). d. Are X, Y independent? justify e. Compute E[XY0or4] f. Find px(8) and P(Y-4X-8).