Random variables X and Y have the joint PMFSe(a² + y²),if x € {1,2,4} and y E {1,3}fx,y(x, y) =0,otherwise(d) What is P(Y = X)?(e) What is P(Y = 3)?(f) Find the marginal PMFS px(x) and py (y).(g) Find the expectations E[X], E[Y] and E[XY].(h) Find the variances Var(X), Var(Y) and Var(X +Y).(i) Let A denote the event X >Y. Find E[X | A] and Var(X | A)

Name: Random variables X and Y have the joint PMFSe(a² + y²),if x € {1,2,4}
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Random variables X and Y have the joint PMFSe(a² + y²),if x € {1,2,4} and y E {1,3}fx,y(x, y) =0,otherwise(d) What is P(Y = X)?(e) What is P(Y = 3)?(f) Find the marginal PMFS px(x) and py (y).(g) Find the expectations E[X], E[Y] and E[XY].(h) Find t

Math

Probability

Random variables X and Y have the joint PMF Se(a² + y²), if x € {1,2, 4} and y E {1,3} fx,y (x, y) = otherwise (d) What is P(Y = X)? (e) What is P(Y = 3)? (f) Find the marginal PMFS px(x) and py (y).

Random variables X and Y have the joint PMF Se(a² + y²), if x € {1,2, 4} and y E {1,3} fx,y (x, y) = otherwise (d) What is P(Y = X)? (e) What is P(Y = 3)? (f) Find the marginal PMFS px(x) and py (y).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

See similar textbooks

Similar questions

Altmans z-score Altmans z-score is a financial tool for predicting insolvency in a business. For a certain company, the z-score formula is z=0.84+0.6StockpriceOutstandingsharesTotalliabilty In this exercise, we assume that thre are 45, 000 outstanding shares at a price of 4.80 each. a. Use L, for total liability, in dollard, and give a formula for the z-score for this company. b. Would a larger total liability idicate a better or worese outlook for the company? c. A z-score of 1.81 or lower indicates a high probability of insolvency. What is the smallest value of L that will give a z-score that indicates a high probability on insolvency?
The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3.Determine the marginal pmf of X. Determine the conditional pmf of Y given X=2.
Two random variables X and Y with a joint PDF f(x,y) = Bx+y for 0≤ x ≤6 , 0≤ x ≤7 and constant B Find value of constant B
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below
Discrete random variables X and Y have a joint distribution function F_X, Y (x, y) = 0.10 u(x + 4) u(y - 1) + 0.15u(x + 3)u(y + 5) + 0.17u(x + 1)u(y - 3) + 0.05 u(x) (y - 1) + 0.18u(x - 2) u(y + 2) + 0.23u(x - 3)u(y - 4) + 0.12u(x - 4)u(y + 3) Find: (a) the marginal distributions F_X(x) and F_Y(y) and sketch the two functions, (b) X and Y, and (c) the probability P{-1 < X lessthanorequalto 4, -3 < Y lessthanorequalto 3}.
Consider a random process X(t) defined by 4 X(t) = Ucost + (V + 1)sint, where U and V are independent random variables for which E(U) = E(V) = 0; E (U²) = E (V²) = 1 a) Find the auto covariance function of X(t) b) Is X(t) wide sense stationary? Explain your answer Jf the Wwss process (Y(+ is given by Y(+) - 100 cos(10t where uniformls
Suppose X and Y are continuous random variables such that the pdf is f(x,y)=x+y with 0≤x≤1,0≤y≤1. a)Draw a graph that illustrates the domain of this pdf. b)Find the marginal pdfs of X and Y.c)Compute ux,ux,var x,var y, cov(x,y) ,and pd (Rho d)) Determine the equation of the least squares regression line and draw it on your graph.