Problems1. Consider discrete random variables X and Y [BLAK 1979] with the joint pmf asshown below:YX-1 011-216-112 곪1616Are X and Y independent? Are they uncorrelated?-100 100-19-19-19-19-19-100 100-1

Solution-: We have following table: X\Y -1 0 1 -2 1/16 1/16 1/16 -1 1/8 1/16 1/8 1 1/8…

Answered: 1. Consider discrete random variables X…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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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1. Consider discrete random variables X and Y [BLAK 1979] with the joint pmf as shown below: Y X -1 0 1 -2 -1 1 2 16 16 Are X and Y independent? Are they uncorrelated? -19 11011816 -12-19-12-19 --10-10-19 16 16 16