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| -rw-r--r-- | houdre/hw6.tex | 4 |
1 files changed, 1 insertions, 3 deletions
diff --git a/houdre/hw6.tex b/houdre/hw6.tex index cf6a3a4..c6b02c0 100644 --- a/houdre/hw6.tex +++ b/houdre/hw6.tex @@ -110,9 +110,7 @@ r_\phi^2)}r_\theta r_\phi d\theta dr_\theta d\phi dr_\phi.$$ The joint probability density function of either location is the product of two normal distributions on $x$ and $y$: $$f_{X,Y}(x,y) = {1\over2\pi\sigma^2}e^{-{1\over2\sigma^2}(x^2+y^2)}.$$ -The distance between these two is $D=(X_1-X_0, Y_1-Y_0),$ with a -probability distribution of -$$f_{D_X}(x) = f_{X,Y}(x,y)$$ +The distance from $(0,0)$ is $r$ in a polar coordinate system. Transforming this into polar coordinates gives the Jacobian (with $x=r\cos\theta$ and $y=r\sin\theta$) $$J = \left|\matrix{\pa x\theta&\pa xr\cr\pa y\theta&\pa yr\cr}\right| = |