Question
Take $A$ to be the square with corners at $(0,1),(1,0),(2,1),(1,2)$. Find the marginal densities of $f=\mathbf{1}_{A}$.
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Refer to Exercise $5.11 .$ Find a. the marginal density functions for $Y_{1}$ and $Y_{2}$ b. $P\left(Y_{2} > 1 / 2 | Y_{1}=1 / 4\right)$
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Summary
Evaluate the line integral $f(x+2 y) d x-2 x d y$ along each of the following closed paths, taken counterclockwise: (a) the circle $x^{2}+y^{2}=1$ (b) the square with corners at (1,1),(-1,1),(-1,-1),(1,-1) (c) the square with corners (0,1),(-1,0),(0,-1),(1,0)
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