Explain in detail what's going on in this problem
Explain in detail what's going on in this problem 4. Let X and Y are two...
1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/ x , if 0 < x < 1, 0 < y < x f(x, y) =0, otherwise . Find the covariance of the random variables X and Y . 2.Let X1 be a Bernoulli random variable with parameter p1 and X2 be a Bernoulli random variable with parameter p2. Assume X1 and X2 are independent. What is the variance of the random variable Y...
3. Suppose that Yi and 2 are continuous random variables with joint pdf given by and zero otherwise, for some constant c >。 (a) Find the value of c. (b) Are Yi and Y2 independent ? Justify your answer. (c) Let Y = Yi + ½. compute the probability P(Y 3). (d) Let U and V be independent continuous random variables having the same (marginal) distri- 3 MARKS 1 MARK 3 MARKS bution as Y2. Identify the distribution of random...
Problem 4 (Conditional Expectation and Variance). Suppose the joint distri- bution of (X, Y) is given by the following contingency (row represents x) table 20 points (x,y) 2 4 6 1 0.3 0 0.1 2 0 0.2 0 3 0.1 0 0.3 A) Compute the marginal distributions of X and Y B) Are X and Y independent? Explain. C) Find the conditional distribution of Y given X -1 D) Compute E[Y|X 1] E) Compute EY|X= 2] F Compute E[exp(X)Y|x 2
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 7: Let X and Y be two jointly continuous random variables with joint PDF 4 (x y) otherwise a) Find P(0< Y< 1/2 I x-2) b) For what value of A is it true that P(0 < Y < ½ |X> A)-5/16
Homework help with 7.38 please
Let Xi and X2 be independent random variables, each from a population probability distri- bution with common probability density function: 7.38 x>1 f(x) Find the joint probability density function of Y XXandX
Problem 5 Let X and Y be random variables with joint PDF Px.y. Let ZX2Y2 and tan-1 (Y/X). Θ i. Find the joint PDF of Z and Θ in terms of the joint PDF of X and Y ii. Find the joint PDF of Z and Θ if X and Y are independent standard normal random variables. What kind of random variables are Z and Θ? Are they independent?
Problem 5 Let X and Y be random variables with joint...
Problem 4. Let X and Y be independent Geom(p) random variables. Let V - min(X, Y) and Find the joint mass function of (V, W) and show that V and W are independent
4. Let X and Y be random variables of the continuous type having the joint pdf f(x,y) = 1, 0<x< /2,0 <y sin . (a) Draw a graph that illustrates the domain of this pdf. (b) Find the marginal pdf of X. (c) Find the marginal pdf of Y. (d) Compute plx. (e) Compute My. (f) Compute oz. (g) Compute oz. (h) Compute Cov(X,Y). (i) Compute p. 6) Determine the equation of the least squares regression line and draw it...
Let X and Y be a random variables taking values 1,2, and 3 with joint I/ 01/8 나.rapis. |probabilitiespxY (1, J) given by the matrix shown: 0 1/2 0 1/8 0 1/8 4 pt. Calculate and sketch joint CDF Fxy(i,j). Find px (i) and pr(i) for ii12, 3. Compute P(X2Y). 3 pt