Simulating bivariate distribution?

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To simulate a bivariate distribution Fxy(x,y) using uniformly distributed variables, first determine the marginal distribution of X. Next, draw a simulated value of X based on this marginal distribution. Then, treat Fxy(x0, Y) as a one-dimensional probability density function to simulate a value of Y. This method allows for effective simulation of bivariate distributions, aiding in verifying homework answers. The approach combines marginal and conditional distributions for accurate results.
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Hi:

From the undergraduate study we know that if we want to simulate a random variable x with distribution Fx(x). We just make Fx(x)=u, u is a uniform distributed variable, find Fx inverse of U. Then we just need to plugin u the uniform distributed random variable.

How about we have Fxy(x,y). How do we simulate this distribution if we only have uniformly distributed variables to plugin?

Any clues?

Lee
 
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1. Find the marginal distribution of X.

2. Using a 1-dimensional method, draw a simulated value of X based on the marginal distribution-- say it's x0.

3. Fxy(x0, Y) is a 1-dimensional pdf. Use a 1-dimensional method to simulate a value of Y.
 
cool, now I can build simulation to check my homework answers.
 
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