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shaiguy6
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So if I start with a multivariate distribution f(x,y), I can find the marginal distributions, the conditional probability distributions, all conditional moments, and by the law of iterated expectations, the moments of both X and Y.
It seems to me that I should be able to relate the conditional moments in x to the conditional moments in y. Right? This is mainly coming from intuition. To be a bit more clear. If I have a function V(x,t) and it has all the properties of a joint probability distribution, I can begin to describe its shape by finding the conditional moments in X and in T. But it seems like all of the conditional moments in X should be able to recreate the original function V(x,t) just as well as all the conditional moments in T. I was wondering if this makes any sense at all. I'm not all too familiar with statistics, and feel like a huge dilletent Relatedly, if i want to define a covariance or correlation between my two random variables, x and t, but I only know their joint distribution, V(x,t), then is the way to go about it to comput the first two moments of X and T using the law of iterated expectations, and then find the covariance and correlation that way?Sorry, one final thing. Having a probability distribution p(x) is equivalent to having the infinity of moments of that distribution. My question is, how can you rebuild the probability distribution given all the moments?
Sorry for my ramblings :)
Any help is appreciated.
It seems to me that I should be able to relate the conditional moments in x to the conditional moments in y. Right? This is mainly coming from intuition. To be a bit more clear. If I have a function V(x,t) and it has all the properties of a joint probability distribution, I can begin to describe its shape by finding the conditional moments in X and in T. But it seems like all of the conditional moments in X should be able to recreate the original function V(x,t) just as well as all the conditional moments in T. I was wondering if this makes any sense at all. I'm not all too familiar with statistics, and feel like a huge dilletent Relatedly, if i want to define a covariance or correlation between my two random variables, x and t, but I only know their joint distribution, V(x,t), then is the way to go about it to comput the first two moments of X and T using the law of iterated expectations, and then find the covariance and correlation that way?Sorry, one final thing. Having a probability distribution p(x) is equivalent to having the infinity of moments of that distribution. My question is, how can you rebuild the probability distribution given all the moments?
Sorry for my ramblings :)
Any help is appreciated.
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