Let X and Y have a uniform distribution on the set of

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

ISBN: 9780321923271 41

Solution for problem 9E Chapter 4.3

Probability and Statistical Inference | 9th Edition

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Problem 9E

PROBLEM 9E

Let X and Y have a uniform distribution on the set of points with integer coordinates in S = {(x, y) : 0 ≤ x ≤ 7, x ≤ y ≤ x + 2}. That is, f (x, y) = 1/24, (x, y) ∈ S, and both x and y are integers. Find

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Given that X and Y are uniformly distributed with f(x,y)= $\frac{1}{24}$ ;0 $\leq{}x\leq{}7,$ x $\leq{}$ y $\leq{}$ x+2 on the set of points on the integer coordinate S={(x,y),0 $\leq{}x\leq{}7,$ x $\leq{}$ y $\leq{}$ x+2}.The given uniform distribution is a discrete uniform distribution, since the set S has only a finite number of outcomes with equal probability.