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A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense).

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Based on comments from the OP the question is really asking for product of the two generating functions which is equivalent to asking about the distribution of $Z=X+Y$ where $X$ and $Y$ are independen …
answered Jun 22 '17 by Lucas Roberts
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As pointed out in the comments by @Michael Chrenick and @GeoMatt22 you need to sum the last one, you've written: $$ Var(Y) = Var(\sqrt{n}\bar{X_n}) = Var(\sqrt{n}\frac{1}{n}\sum_{i=1}^n{X_i}) = \fra …
answered Jul 22 '17 by Lucas Roberts
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Not entirely clear to me from reading the comments if the OP has solved this but there is no answer so I will write one. The distribution of each $Y_i$ will be normal with given means and variances: …
answered Jul 24 '17 by Lucas Roberts
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You are using the correct approach with the total variance law. $$\mathbb{V}ar(X)= \mathbb{V}ar(\mathbb{E}(X|Q)) + \mathbb{E}(\mathbb{V}ar(X|Q) ).$$ Here you will need the expectations and varianc …
answered Jul 22 '17 by Lucas Roberts
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I'm not sure if you can say something for every $n$ (and all distributions) for Hoeffding precisely. For Chernoff you can say that the moment bound is tighter than the Chernoff bound. In the linked pa …
answered Sep 10 '18 by Lucas Roberts
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You have 12 in your sixth arrow should this be 1/2? If this is a typo (either in your slides or this post) then the rest of the problem seems straightforward, multiply by 2 to get $2y(x)=y(x+1) +y(x …
answered Nov 12 '17 by Lucas Roberts
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If you condition on (fix) the value of $X$, then the expectation you are calculating is $\mathbb{E}(Y|X)=\int XY dP(Y|X)$ and you may safely move $X$ to the left hand side (outside the integral) becau …
answered Mar 22 '18 by Lucas Roberts
6
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as pointed out in the comments by @zhanxiong, the triangle inequality is sufficient here, take: $|X_1 -X_2| \leq |X_1| +|X_2|$ and take expectations to get $\mathbb{E}(|X_1 -X_2|) \leq \mathbb{E}(|X …
answered Jan 5 '18 by Lucas Roberts
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Using iterated expectations and law of total variance here is the approach I would use as recommended by @Glen_b in the comments above. To use these you need the means and variances of the individual …
answered Jul 22 '17 by Lucas Roberts