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(1) If the joint density of Y₁ and Y₂ is given by: 1 2 and ƒ (Y₁,Y₂)=e¯(Y₁+Y₂) for y₁ > 0, y ₂ > 0 U = Y 1 +Y/₂ 2 2 find the density function of U using the method of Cumulative Distribution Functions (CDF's) Method.

(1) If the joint density of Y₁ and Y₂ is given by: 1 2 and ƒ (Y₁,Y₂)=e¯(Y₁+Y₂) for y₁ > 0, y ₂ > 0 U = Y 1 +Y/₂ 2 2 find the density function of U using the method of Cumulative Distribution Functions (CDF's) Method.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Homework Assignment 1 MAT 282 Statistical Inference (1) If the joint density of Y₁ and Y, is given by: 1 2 and ƒ (Y ₁,Y ₂) = e¯(³₁+Y₂) for y₁ > 0, y ₂ > 0 1⁹ 2 U = Y₁+Y 1 2 f (x, y) = – find the density function of U using the method of Cumulative Distribution Functions (CDF's) Method. 2 (2) Let X be the amount of premium gasoline (in 1.000 gallons) that a service station has in its tanks at the beginning of a day, and Y the amount which the service station sells during that day. If the joint density of X and Y is given by: 1 for 0<y < x < 20 200 1 elsewhere use the distribution function technique to find the probability density of the amount that the service station has left in its tanks at the end of the day.
Transcribed Image Text:Homework Assignment 1 MAT 282 Statistical Inference (1) If the joint density of Y₁ and Y, is given by: 1 2 and ƒ (Y ₁,Y ₂) = e¯(³₁+Y₂) for y₁ > 0, y ₂ > 0 1⁹ 2 U = Y₁+Y 1 2 f (x, y) = – find the density function of U using the method of Cumulative Distribution Functions (CDF's) Method. 2 (2) Let X be the amount of premium gasoline (in 1.000 gallons) that a service station has in its tanks at the beginning of a day, and Y the amount which the service station sells during that day. If the joint density of X and Y is given by: 1 for 0<y < x < 20 200 1 elsewhere use the distribution function technique to find the probability density of the amount that the service station has left in its tanks at the end of the day.
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