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Mathematics
Set Theory, Logic, Probability, Statistics
Proving a multivariate normal distribution by the moment generating function
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[QUOTE="StoneTemplePython, post: 5870012, member: 613025"] They also show the convolution of two normal r.v.'s directly here: [URL]https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-11-derived-distributions-convolution-correlation/MIT6_041F10_L11.pdf[/URL] (MIT is not very big on moment generating functions. ) - - - - To be clear the outline I gave [I]was[/I] mathematical. You'd just need to recut it into a couple of lemmas, then carefully use induction in the main argument. The underlying idea that comes up over and over (in both part 1 and part 2) is that convolving a random variable with a scaled down version of itself is just a rescaling. And convolving a normal r.v. with an independent normal r.v. results in a normal r.v. There would only be one or two equations here -- and it has a linear algebra flair in that everything we're interested in is written as a linear combination of a scaled version of identical random normals (i.e. rescaling) and independent normals. It's actually a very simple idea. - - - - You seem to be quite keen on using MGFs which is not how I'd look at this. Good luck. [/QUOTE]
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Proving a multivariate normal distribution by the moment generating function
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