MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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?
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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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