ProbabilityFor each observation pairExample 5-31. A random observation ona bivariate population (X, Y) can yield one of the (1, 1) ; (2, 1) ; (3, 3 ) ; (4, 3)following pairs of values with probabilities1noted against them :1201(3, 1) ; (4, 1) ; (1, 2) ; (2, 2) ;(3, 2); (4, 2); (1, 3) ; (2, 3)10Find the probability that Y = 2 given that X = 4. Also find the probability that Y = 2. Examineif the two events X = 4 and Y = 2 are independent.%3D%3D%3D

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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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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.
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