Let A ⊂ R2 be the triangle with vertices (0, 0), (1, 0) and (0, 1). They (X, Y ) are uniformly distributed in A. (a) Determine the probability density of (X,Y ). (b) Show that X and Y are dependent. Provide both an intuitive reasoning and a formal proof. (c) The distribution function of X for 0 ≤ x ≤ 1 is given by FX(x) = 2x −x2 Show this in two ways: (i) using the probability density and (ii) by means of a direct area calculation.

Let A ⊂ R2 be the triangle with vertices (0, 0), (1, 0) and (0, 1). They (X, Y ) are uniformly distributed in A. (a) Determine the probability density of (X,Y ). (b) Show that X and Y are dependent. Provide both an intuitive reasoning and a formal proof. (c) The distribution function of X for 0 ≤ x ≤ 1 is given by FX(x) = 2x −x2 Show this in two ways: (i) using the probability density and (ii) by means of a direct area calculation.

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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