1, 0< yı, Y2 1 | 0, clsewhere f(y1, Y2) %3D Are random variables Y and Y, independent? Show the rcasoning bchind your conclusion. (b) Suppose now that Y1 and Y2 are probabilities such that Y1 + Y2 < 1. A valid joint distribution for these random variables is 2, 0< y1, Y2 < 1, y1 + Y2 <1 0, clsewhere f(y1, 42) = Are the random probabilities Y1 and Y2 independent? Show the reasoning behind your conclusion.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 34CR
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(a) The bivariate uniform distribution on the unit square is given by
1, 0<y1, Y2<1
0, clsewhere
f(y1, Y2) =
Are random variables Y and Y, independent? Show the rcasoning behind your conclusion.
(b) Suppose now that Y1 and Y, are probabilities such that Yı + Y2 < 1. A valid joint
distribution for these random variables is
{
S 2, 0< y1, Y2 < 1, y1 + y2 < 1
0, elsewhere
f(y1, 42)
Are the random probabilitics Yı and Y, independent? Show the reasoning behind your
conclusion.
Transcribed Image Text:(a) The bivariate uniform distribution on the unit square is given by 1, 0<y1, Y2<1 0, clsewhere f(y1, Y2) = Are random variables Y and Y, independent? Show the rcasoning behind your conclusion. (b) Suppose now that Y1 and Y, are probabilities such that Yı + Y2 < 1. A valid joint distribution for these random variables is { S 2, 0< y1, Y2 < 1, y1 + y2 < 1 0, elsewhere f(y1, 42) Are the random probabilitics Yı and Y, independent? Show the reasoning behind your conclusion.
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