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## Wednesday, October 29, 2014

### conditional independence, learning notes

Remember -- Discrete is always easier to understand ...

Q: does conditional independence imply unconditional independence?

Simple example - among guys, weight is unrelated to income - conditional independence, but removing the condition, among all genders weight has a bearing on income.

However, in this math problem the terminology can be confusing - Given W = w, the 2 random variables X and Y are conditionally iid exp(w) distributed. W itself follows a G(alpha, beta) distribution. Are X and Y unconditionally independent?

I feel the key is the symbol "w", which is neither a variable nor a number, but rather a configurable parameter. In the noisegens, this w is a constant, like 39.8. However, as operator of the noisegen, we could set this parameter and potentially modify the distribution(s).

If for all w values, X and Y are independent, then I believe X and Y are unconditionally independent.