**1. Let \( X \) and \( Y \) be jointly continuous random variables with joint pdf**\[f_{X,Y}(x,y) = \begin{cases} \exp(-2x - y) + \exp(-x - 2y) & \text{if } x,y > 0 \\ 0 & \text{otherwise} \end{cases}\]**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* \[\int x \cdot e^{-ax} \, dx = \frac{(-1 - ax) \cdot e^{-ax}}{a^2} + C.\]

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

Answered: 1. Let X and Y be jointly continuous…

A First Course in Probability (10th Edition)

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Page 263, 4.4.8
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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.