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Let (X,Y) be a 2D random variable that is uniformly distributed inside the ellipse defined by the equation | Let (X,Y) be a 2D random variable that is uniformly distributed inside the ellipse defined by the equation | ||
| − | <math>\frac{x}{a}+\frac{y}{b}=1,</math> | + | <math>(\frac{x}{a})^{2}+(\frac{y}{b})^{2}=1,</math> |
for some constants a,b>0. Find the conditional probability density function <math>f_{X|Y}(x|y).</math> | for some constants a,b>0. Find the conditional probability density function <math>f_{X|Y}(x|y).</math> | ||
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===Answer 1=== | ===Answer 1=== | ||
| − | + | Hint: | |
| + | :Same as the second problem. | ||
| + | : Area of the ellipse is <math>\pi ab</math> | ||
===Answer 2=== | ===Answer 2=== | ||
Write it here. | Write it here. | ||
Latest revision as of 11:00, 26 March 2013
Contents
Practice Problem: What is the conditional density function
Let (X,Y) be a 2D random variable that is uniformly distributed inside the ellipse defined by the equation
$ (\frac{x}{a})^{2}+(\frac{y}{b})^{2}=1, $
for some constants a,b>0. Find the conditional probability density function $ f_{X|Y}(x|y). $
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
Hint:
- Same as the second problem.
- Area of the ellipse is $ \pi ab $
Answer 2
Write it here.
Answer 3
Write it here.
