4.3-8. (a) Find a constant b (in terms of a) so that the function be (x+y) 1) = { bc and 0 fx, y(x, y) = 0

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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4.3-8. (a) Find a constant b (in terms of a) so that the function
be-(x+y)
- {8
0
fx, y(x, y) =
4.3-9 (a) Ru
0 < x <a and
elsewhere
is a valid joint density function.
(b) Find an expression for the joint distribution function.
0<y<∞
Transcribed Image Text:4.3-8. (a) Find a constant b (in terms of a) so that the function be-(x+y) - {8 0 fx, y(x, y) = 4.3-9 (a) Ru 0 < x <a and elsewhere is a valid joint density function. (b) Find an expression for the joint distribution function. 0<y<∞
4.2-10. Discrete random variables X and Y have a joint distribution function
Fx, y(x, y) = 0.10u(x+4)u(y-1) +0.15u(x + 3)u(y + 5)
+0.17u(x + 1)u(y - 3) +0.05u(x)u(y - 1)
+0.18u(x - 2)u(y + 2) +0.23u(x - 3)u(y-4)
+0.12u(x-4)u(y + 3)
Find: (a) the marginal distributions Fy(x) and Fy(y) and sketch the two
functions, (b) X and Y, and (c) the probability P{-1 < X < 4, -3 < Y ≤ 3}.
Transcribed Image Text:4.2-10. Discrete random variables X and Y have a joint distribution function Fx, y(x, y) = 0.10u(x+4)u(y-1) +0.15u(x + 3)u(y + 5) +0.17u(x + 1)u(y - 3) +0.05u(x)u(y - 1) +0.18u(x - 2)u(y + 2) +0.23u(x - 3)u(y-4) +0.12u(x-4)u(y + 3) Find: (a) the marginal distributions Fy(x) and Fy(y) and sketch the two functions, (b) X and Y, and (c) the probability P{-1 < X < 4, -3 < Y ≤ 3}.
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