- #1

gajohnson

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## Homework Statement

A point is chosen randomly in the interior of an ellipse:

(x/a)^2 + (y/b)^2 = 1

Find the marginal densities of the X and Y coordinates of the points.

## Homework Equations

NA

## The Attempt at a Solution

So this ought to be uniformly distributed, thus the density function for [itex](x,y)[/itex] is [itex]f_{x,y}[/itex] = [itex]1/∏ab[/itex] (where ∏ab is the area of the ellipse)

So, to find the marginal density for x (and later for y), I realize that I just need to find the limits of integration and then go about my business. I believe that the limits of integration are

[itex]-(b/a)\sqrt{a^2 - x^2}[/itex] and [itex]b/a\sqrt{a^2 - x^2}[/itex],

since these should be the minimum and maximum values that y can take for any given x. Are these limits of integration and/or is my reasoning correct?

As always, many thanks to all of you wonderful Homework Helpers!

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