Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2...

Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2 ; 0 < y1 <y2 <1,

where k is a constant equal to 8.

a) Find the conditional expected value and variance of Y1 given Y2=y2.

b) Are Y1 and Y2 independent? Justify your answer.

c) Find the covariance and correlation between Y1 and Y2.

d) Find the expected value and variance of Y1+Y2.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose that Y1 and Y2 are jointly distributed with joint pdf: f(y1,y2) ={cy2. for 0 ≤...

Suppose that Y1 and Y2 are jointly distributed with joint pdf: f(y1,y2) ={cy2. for 0 ≤ y1 ≤ y2 ≤ 1 0. otherwise} (1) Find c value. (2) Are Y1 and Y2 independent? Justify your answer. (3) ComputeCov(Y1,Y2). (4) Find the conditional density of Y1 given Y2=y2. (5) Using (d), find the conditional expectation E (Y1|Y2). (6) Suppose that X1=Y1+Y2, and X2= 2Y2. What is the joint density ofX1andX2?

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1, Y2). c) Find V(Y1−Y2). d) Find Var(Y1|Y2=y2).

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤...

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, y1 + y2 ≤ 1, y1 − y2 ≥ −1, 0, otherwise a. Find the value of k that makes this a probability density function. b. Find the probabilities P(Y2 ≤ 1/2) and P(Y1 ≥ −1/2, Y2 ≤ 1/2 c. Find the marginal distributions of Y1 and of Y2. d. Determine if Y1 and Y2 are independent e....

The joint pdf of a two continuous random variables is given as follows: ??,? (?, ?)...

The joint pdf of a two continuous random variables is given as follows: ??,? (?, ?) = { ??? 0 < ? < 2, 0 < ? < 1 0 ??ℎ?????? 1) Find c. 2) Find the marginal PDFs of ? and ?. Make sure to write the ranges. Are these random variables independent? 3) Find ?(0 < ? < 1|0 < ? < 1) 4) What is ??|? (?|?). Make sure to write the range of ?.

Suppose X and Y are random variables with joint density f(x, y) = c(x2y + y2),...

Suppose X and Y are random variables with joint density f(x, y) = c(x2y + y2), − 1 ≤ x ≤ 1, 0 ≤ y ≤ 1 (0 else). a) Find c. b) Determine whether X and Y are independent. c) Compute P(3X + 2Y > 1 | −1/2 ≤ X ≤ 1/2).

The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ??...

The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ?? -8x^2-18y^2 a) Find the mean and variance of ? and ? and the value of ?. b) Determine if ? and ? are independent. c) Determine the distribution of ? and ?.

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF...

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF of (R,S)? Prove that R and S are are independent standard normal random variables. R = sqrt(-2logA)*cos(2piB) S = sqrt(-2logA)*sin(2piB)

Suppose A and B are independent uniform random variables on [0,1]. What is the joint PDF...

Suppose Y1,Y2, .. ,Y8 are independent and identically distributed as Poisson random variables with mean lambda....

Suppose Y1,Y2, .. ,Y8 are independent and identically distributed as Poisson random variables with mean lambda. a) Derive the most powerful test for testing Ho: lambda = 2, Ha: lambda = 3. Carefully show all work involved in the derivation. i) Give the form of the test. (In other words, for what general values of Y1,Y2, .. ,Y8 will Ho be rejected?) ii) Describe the rejection region as carefully as possible if alpha <= .05 (and is as close as...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) =...

The joint probability density function (PDF) of two random variables (X,Y) is given by ???(?,?) = { 1, 0 ≤ ? ≤ 2,0 ≤ ? ≤ 1,2? ≤ ? 0, otherwise 1) Find the correlation coefficient ??? between the two random variables X and Y Find the probability P(Y>X/2). help please asap

Subjects