An article describes a model for the movement of a particle. Assume that a particle moves within the region bounded by the x-axis from 0 to 1 and y-axis from 0 to 1. Let (x.y) denote the position of the particle at a given time. The joint density of X and Y is given by: fx.x (x, y) = kx²(1 – x)y² for 0

An article describes a model for the movement of a particle. Assume that a particle moves within the region bounded by the x-axis from 0 to 1 and y-axis from 0 to 1. Let (x.y) denote the position of the particle at a given time. The joint density of X and Y is given by: fx.x (x, y) = kx²(1 – x)y² for 0

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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Question

4.
An article describes a model for the movement of a particle. Assume that a
particle moves within the region bounded by the x-axis from 0 to 1 and y-axis from 0 to 1.
Let (x.y) denote the position of the particle at a given time. The joint density of X and Y
is given by:
fx.x (x, y) = ka²(1 – x)y²
for 0 < r < 1,0 < y < 1
(a) Find k.
(b) Find the joint cdf of (X, Y).
(c) Find the Marginal pdf of X and of Y.
(d) Are X and Y independent.
(e) Find the conditional pdf of Y given X i.e. fy(y|r).

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