Suppose that (X,Y) on [0, 1]² have the bivariate cumulative distribution function F(x, y) := xy{1+ 0(1 – x)(1 – y)} for 0
Suppose that (X,Y) on [0, 1]² have the bivariate cumulative distribution function F(x, y) := xy{1+ 0(1 – x)(1 – y)} for 0
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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![Suppose that (X,Y) on [0, 1]² have the bivariate cumulative distribution function
F(x, y) := xy{1+ 0(1 – x)(1 – y)}
-
for 0 < x, y < 1 and |0| < 1.
(a) Find the joint density f(x, y) of (X, Y) on [0, 1]².
(b) Find the (marginal) density of X. (Which is the same as the marginal density of Y.)
(c) Find the mean and variance of X (and thus also of Y).
(d) Find the covariance and correlation of X and Y.
1
i=1
(e) Say X1,...,
Σ X?. Find Cov (X, Χ.).
Xn are i.i.d. from the distribution of X above. Let Xn
Ε Σ Χ. and X .
1
n
(f) What does Xn converge to in probability (as n gets large)? What does X2n converge to?
(g) What is the asymptotic distribution of Xn?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d65f259-146b-4e7b-895c-9b88cd9e86d3%2F5a87eaa0-2dd6-403b-b2e4-230b7cef47eb%2Fgndscbi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that (X,Y) on [0, 1]² have the bivariate cumulative distribution function
F(x, y) := xy{1+ 0(1 – x)(1 – y)}
-
for 0 < x, y < 1 and |0| < 1.
(a) Find the joint density f(x, y) of (X, Y) on [0, 1]².
(b) Find the (marginal) density of X. (Which is the same as the marginal density of Y.)
(c) Find the mean and variance of X (and thus also of Y).
(d) Find the covariance and correlation of X and Y.
1
i=1
(e) Say X1,...,
Σ X?. Find Cov (X, Χ.).
Xn are i.i.d. from the distribution of X above. Let Xn
Ε Σ Χ. and X .
1
n
(f) What does Xn converge to in probability (as n gets large)? What does X2n converge to?
(g) What is the asymptotic distribution of Xn?
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