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f(x, y) = axyI(0,1) (x)I(0,²) (y) 59. Given this joint pdf, (a) Find the value of a that makes this a valid pdf. (b) Find P(X ≤ 1/2, Y ≤ 1/2). (c) Find the marginal distribution of X, fx (r). (d) Find the marginal distribution of Y, fy (y). (e) Find P(Y ≤ 1/2).

f(x, y) = axyI(0,1) (x)I(0,²) (y) 59. Given this joint pdf, (a) Find the value of a that makes this a valid pdf. (b) Find P(X ≤ 1/2, Y ≤ 1/2). (c) Find the marginal distribution of X, fx (r). (d) Find the marginal distribution of Y, fy (y). (e) Find P(Y ≤ 1/2).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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Suppose the location of a particle in the plane is restricted to be within the region of the first quadrant enclosed by y = 0, y = x², and x = 1 and that the x- and y- coordinates of the point are described by the jointly continuous random variables X and Y, respectively, with joint pdf f(x, y) = axyI(0,1)(x) I(0,z²) (y) 59. Given this joint pdf, (a) Find the value of a that makes this a valid pdf. (b) Find P(X ≤ 1/2, Y ≤ 1/2). (c) Find the marginal distribution of X, fx(x). (d) Find the marginal distribution of Y, fy (y). (e) Find P(Y≤ 1/2).
Transcribed Image Text:Suppose the location of a particle in the plane is restricted to be within the region of the first quadrant enclosed by y = 0, y = x², and x = 1 and that the x- and y- coordinates of the point are described by the jointly continuous random variables X and Y, respectively, with joint pdf f(x, y) = axyI(0,1)(x) I(0,z²) (y) 59. Given this joint pdf, (a) Find the value of a that makes this a valid pdf. (b) Find P(X ≤ 1/2, Y ≤ 1/2). (c) Find the marginal distribution of X, fx(x). (d) Find the marginal distribution of Y, fy (y). (e) Find P(Y≤ 1/2).
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