Suppose x and y are two random variables. If y= 3x -2 then the mathematical expectations...

Question

Question

Suppose x and y are two random variables. If y= 3x -2 then the mathematical expectations and variances of x and y are related as follows

math Statistics-And-Probability

Answer 1

Answer #1

As we have Ya 3x-2 ) JE 21573 tiss (afreda a Elant b and vitl= (3, vizu VIV) grla vlaxtb) = a) PV12 to option I do is correct

Answer 2

Similar Homework Help Questions

13. Consider the random variables X and Y with the following expectations: E(X)= 2, E(Y)=1 E(X²)=15,...

13. Consider the random variables X and Y with the following expectations: E(X)= 2, E(Y)=1 E(X²)=15, E(Y2)=9, E(XY)=1. Let U = X + 2Y, V = 3X - Y and calculate the covariance of U and V.
Two random variables X and Y have means E[X] = 1 and E[Y] = 0, variances...

Two random variables X and Y have means E[X] = 1 and E[Y] = 0, variances 0x2 = 9 and Oy2 = 4, and a correlation coefficient xx =0.6. New random variables are defined by V = -2X + Y W = 2X + 2Y Find the means of V and W Find the variances of V and W defined in question 3 Find Rww for the variables V and W defined in question 3
6.48 Two Gaussian random variables, X and Y, are in- dependent. Their respective means are 4...

6.48 Two Gaussian random variables, X and Y, are in- dependent. Their respective means are 4 and 2, and their respective variances are 3 and 5 (a) Write down expressions for their marginal pdfs. (b) Write down an expression for their joint pdf. (c) What is the mean of Z 3X +Y? Z, 3X- Y? (d) What is the variance of Z = 3X + Y? Z, 3X-Y? (e) Write down an expression for the pdf of Z1 3X+Y

Consider two random variables, X and Y. Let E(X) and E(Y) denote the population means of...

Consider two random variables, X and Y. Let E(X) and E(Y) denote the population means of X and Y respectively. Further, let Var(X) and Var(Y) denote the population variances of X and Y. Consider another random variable that is a linear combination of X and Y Z- 3X- Y What is the population variance of Z? Assume that X and Y are independent, which is to say that their covariance is zero.
Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.3...

Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.3 50 80 0.2 30 50 0.5 40 60 (a) Compute the expected value and the variance for x and y. E(x) = E(y) = Var(x) = Var(y) = (b) Develop a probability distribution for x + y. x + y f(x + y) 130 80 100 (c) Using the result of part (b), compute E(x + y) and Var(x + y). E(x...
2) Two statistically-independent random variables, (X,Y), each have marginal probability density,...

2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector, 2) Two statistically-independent random variables, (X,Y), each have marginal probability density, N(0,1) (e.g., zero-mean, unit-variance Gaussian). Let V-3X-Y, Z = X-Y Find the covariance matrix of the vector,

[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x...

[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))
Suppose the joint probability distribution of two binary random variables X and Y are given as...

Suppose the joint probability distribution of two binary random variables X and Y are given as follows. X/Y 1 0 1 2 1 4 0 + 1 (a) Show the marginal distribution of X. [2pts] (b) Find entropy H(Y). [2pts] (e) Find conditional entropy H(XY). (3pts] (d) Find mutual information I(X;Y). [3pts] 2 (e) Find joint entropy H(X,Y). (3pts) Note: The following three proofs are not related to the example in parts (a - e). You need to prove each...
9. Suppose the discrete random variables X and Y are jointly distributed according to the following...

9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Y|Y -1 0 1 0.1 0.1 0.1 3 0 0.2 0.1 4. 0.2 0.1 0.1 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]

2. Let X and Y be continuous random variables with joint pdf fx.y (x. y)- 3x,...

2. Let X and Y be continuous random variables with joint pdf fx.y (x. y)- 3x, 0 Syx, and zero otherwise. a. b. c. d. e. What is the marginal pdf of X? What is the marginal pdf of Y? What is the expectation of X alone? What is the covariance of X and Y? What is the correlation of X and Y?