MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:Let f (x, y) = e-8-Y for x > 0 and y > 0 be a joint pdf of x and y. Prove that these two
variables are independent random variables. (HINT: Review the definition of independence.)
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Based on the above information we prove that X and Y are independent random variables.
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- a and b onlyarrow_forwardThe random variables X and Y have the joint density: fX,Y(x,y) = 2−x−y, for 0<x<1, 0<y<1 0, otherwise For each of the following, please provide your answers in three decimal places: (a) What is the expected value of X? (b) What is the variance of X? (c) What is the covariance of X and Y? (d) What is the correlation of X and Y?arrow_forwardX is the Gaussian (μ=1, σ=2) random variable. Y is the Gaussian (μ=2, σ=4) radnom variable. X and Y are independent. a) What is the PDF of V = X + Y b) What is the PDF of W = 3X + 2Yarrow_forward
- Suppose X and Y are independent random variables, where X is uniform on (0,1), and Y is exponential with mean 1/3. Let Z = min{X,Y}. Let f(c) denote the pdf of Z. What is f(1/6)? (You may use the approximation e ~ 2.718.) a) 2.12. b) 3.01. c) 4.42. d) 5.07. e) None of the above.arrow_forwardConsider random variables Xand Y with following joint pdf given as f(x,y) ={x+y 0≤x≤1, 0≤y≤1, 0 elsewhere. Compute correlation coefficient, ρXYarrow_forwardLet X and Y be discrete random variables with joint pdf f(x,y) given by the following table: y = 1 y = 2 y = 3 x = 1 0.1 0.2 0 x = 2 0 0.167 0.4 x = 3 0.067 0.022 0.033 Find the marginal pdf’s of X and Y. Are X and Y independent?arrow_forward
- Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere ] What is the joint CDF of X and Y? Note: F(x,y) = P(X<=x, Y<=y) = ∫ ∫ f(x,y)dxdyarrow_forwardShow complete solution: Assume that X and Y are independent random variables where X has a pdf given by fx(x) = 2x1(0,1) (x) and Y has a pdf given by fy(y) = 2(1 — y)I(0,1)(y). Find the distribution of X+Y.arrow_forwardShow that if X, Y are independent random variables, then Cov(X, Y ) = 0.arrow_forward
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