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Refer to Exercise 5.11. Finda the marginal density
Chapter 5, Problem 29E(choose chapter or problem)
Refer to Exercise 5.11. Find
a) the marginal density functions for \(Y_{1}\) and \(Y_{2}\).
b) \(P\left(Y_{2}>1 / 2 \mid Y_{1}=1 / 4\right)\).
Questions & Answers
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QUESTION:
Refer to Exercise 5.11. Find
a) the marginal density functions for \(Y_{1}\) and \(Y_{2}\).
b) \(P\left(Y_{2}>1 / 2 \mid Y_{1}=1 / 4\right)\).
ANSWER:Step 1 of 3
(a). Suppose \(Y_{1}\) and \(Y_{2}\) are uniformly distributed over the triangle shown below
To find the marginal density functions for \(Y_{1}\) and \(Y_{2}\)
From the figure given above, it is seen that \(y_{2} \geq 0\) is always and \(-1 \leq y_{1} \leq 1\). Therefore, the region is enclosed by the curve
\(\left|y_{1}\right|+y_{2}=1\) (i)
From equation (i), we have
\(y_{2}=1-\left|y_{1}\right|\)
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