Let A be a "random point" that coincides with the point a₁, a2, a3 or a4 with equal probabil- ities. Y
Let A be a "random point" that coincides with the point a₁, a2, a3 or a4 with equal probabil- ities. Y
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Solution Ll part
![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.
(a) Find the joint distribution of random variables X and Y.
(b) Find the marginal distribution of X and Y.
(c) Find the cumulative distribution functions of X and Y.
(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%2Fc3334afc-a11d-4f09-ab81-c3d59c62e237%2Fxjsw51q_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.
(a) Find the joint distribution of random variables X and Y.
(b) Find the marginal distribution of X and Y.
(c) Find the cumulative distribution functions of X and Y.
(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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