Homework Assignment 1MAT 282Statistical Inference(1) If the joint density of Y₁ and Y, is given by:12andƒ (Y ₁,Y ₂) = e¯(³₁+Y₂) for y₁ > 0, y ₂ > 01⁹2U =Y₁+Y12f (x, y) =–find the density function of U using the method of Cumulative DistributionFunctions (CDF's) Method.2(2) Let X be the amount of premium gasoline (in 1.000 gallons) that a servicestation has in its tanks at the beginning of a day, and Y the amount which theservice station sells during that day. If the joint density of X and Y is givenby:1 for 0

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(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: f (x,y) =< 200 0 for 0

(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: f (x,y) =< 200 0 for 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question

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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