EXER 6.3Find the covariance and the correlation coefficient between Xand Y, if X and Y are jointly discrete random variables, withjoint PMF given by: SHOW SOLUTIONSX\Y0160286128203333332828282120280

For the given data Find the covariance and correlation between x and y

Answered: Find the covariance and the correlation…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
Suppose the random variables X,, X,,X3 have the population variance/covariance matrix: -2 0 E=-2 5 1 Calculate the principal components and interpret their meaning. What can be gained from knowing these values?
If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+1)²] = 33. Then the values of u and o are: %3D %3D u = 3 and o = V17 u = 6 and o = 3 and o=32 3/5 and o=6
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We have the following information about the random variables X and Y: |x = 1, |y = −1.5 , ox = 0.25, c} = 1. o Calculate the variance of Z = 3X + 5Y, a) when the coefficient of correlation is p(X, Y) = 0.46: 0²77 34.15 Z b) when X and Y are independent random variables: 0²2 27.75 X
Consider the following joint random variable pmf for X and Y: x y -1 0 1/4 0 1 1/8 1 1 1/2 1 0 1/8 What is the correlation of X and Y?
Let X,, X2, and X3 be independent random variables, each are binomially distributed with n = 100 and p = 0.2. Let A = X,– 2X2 and B = X3 + 3X1. Find PAB- %3D %3D
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Two computer companies are offering new software to universities. Let X and Y denote the number of software installed in three major universities by these two companies. Suppose that the variance of X is 583, the variance of Y is 752, and the covariance of X and Y is 179. a) Calculate the correlation coefficient (p) Select one: a. o.825 b. 0.270 c. 0.532 d. None of the answers

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Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 2 3 6 0 28 28 28 9 6 1 0 28 28 3 2 0 0 28