1. Let X and Y be jointly continuous random variables with joint pdf{exp(-(exp(-2x - y) + exp(-x-2y)x,y> 00 otherwisefx,y (x, y) =a. Find the MAP estimate of X given Y = y.b. Find the ML estimate of X given Y = y.You may use the fact that fx e-ax dx=(-1-ax)-e-axa²+ C.

Given that the joint pdf of the continuous random variables X and Y as

1. Let X and Y be jointly continuous random variables with joint pdf fxy(x, y) = (exp(-2x − y) + exp(-x-2y) x,y>0 - 0 otherwise a. Find the MAP estimate of X given Y = y. b. Find the ML estimate of X given Y = y.

1. Let X and Y be jointly continuous random variables with joint pdf fxy(x, y) = (exp(-2x − y) + exp(-x-2y) x,y>0 - 0 otherwise a. Find the MAP estimate of X given Y = y. b. Find the ML estimate of X given Y = y.

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.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

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Question

1. Let X and Y be jointly continuous random variables with joint pdf
{exp(-
(exp(-2x - y) + exp(-x-2y)
x,y> 0
0 otherwise
fx,y (x, y) =
a. Find the MAP estimate of X given Y = y.
b. Find the ML estimate of X given Y = y.
You may use the fact that fx e-ax dx
=
(-1-ax)-e-ax
a²
+ C.

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