(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

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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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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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