Let a random variable X be the first coordinate of the point A, a random variable Y be the second coordinate of the point A. (d) Compute E[X] and E[Y]. (e) Compute Var[X], Var[Y], Cov(X, Y), Corr (X, Y). (f) Find the conditional distribution of Y given X = -1,0, 1. (g) Compute E[Y|X = −1], E[Y|X = 0], E[Y|X = 1]. (h) Characterize a random variable E[Y|X]. (i) Verify the Law of Iterated Expectations by checking E[Y] = E[E[Y|X]]. (j) Is the point with coordinates (E[X], E[Y]) in the support of A? (k) Are the random variables X and Y correlated? Independent? Discuss. (1) What would the joint distribution be if the random variables X and Y are independent and their marginal distributions do not change.
Let a random variable X be the first coordinate of the point A, a random variable Y be the second coordinate of the point A. (d) Compute E[X] and E[Y]. (e) Compute Var[X], Var[Y], Cov(X, Y), Corr (X, Y). (f) Find the conditional distribution of Y given X = -1,0, 1. (g) Compute E[Y|X = −1], E[Y|X = 0], E[Y|X = 1]. (h) Characterize a random variable E[Y|X]. (i) Verify the Law of Iterated Expectations by checking E[Y] = E[E[Y|X]]. (j) Is the point with coordinates (E[X], E[Y]) in the support of A? (k) Are the random variables X and Y correlated? Independent? Discuss. (1) What would the joint distribution be if the random variables X and Y are independent and their marginal distributions do not change.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
![Economics
Let A be a "random point" that coincides with the point a1, a2, a3 or a4 with equal probabil-
ities.
a3
1
-1
Y
a2
0
as
1 ai
X
Let a random variable X be the first coordinate of the point A, a random variable Y be the
second coordinate of the point A.
(d) Compute E[X] and E[Y].
(e) Compute Var[X], Var[Y], Cov(X, Y), Corr (X, Y).
(f) Find the conditional distribution of Y given X = -1,0, 1.
(g) Compute E[Y|X = −1], E[Y|X = 0], E[Y|X = 1].
(h) Characterize a random variable E[Y|X].
(i) Verify the Law of Iterated Expectations by checking E[Y] = E[E[Y|X]].
(j) Is the point with coordinates (E[X], E[Y]) in the support of A?
(k) Are the random variables X and Y correlated? Independent? Discuss.
(1) What would the joint distribution be if the random variables X and Y are independent
and their marginal distributions do not change.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcca31329-ec54-42d3-a2c8-7bca24f8b719%2F2bdb43d5-612a-4ac6-9a96-4e9a670e6338%2Fmvcys9l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Economics
Let A be a "random point" that coincides with the point a1, a2, a3 or a4 with equal probabil-
ities.
a3
1
-1
Y
a2
0
as
1 ai
X
Let a random variable X be the first coordinate of the point A, a random variable Y be the
second coordinate of the point A.
(d) Compute E[X] and E[Y].
(e) Compute Var[X], Var[Y], Cov(X, Y), Corr (X, Y).
(f) Find the conditional distribution of Y given X = -1,0, 1.
(g) Compute E[Y|X = −1], E[Y|X = 0], E[Y|X = 1].
(h) Characterize a random variable E[Y|X].
(i) Verify the Law of Iterated Expectations by checking E[Y] = E[E[Y|X]].
(j) Is the point with coordinates (E[X], E[Y]) in the support of A?
(k) Are the random variables X and Y correlated? Independent? Discuss.
(1) What would the joint distribution be if the random variables X and Y are independent
and their marginal distributions do not change.
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