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1 vote

Confusion in using applying variance formula

The variance of a sum of independent random variables $X$ and $Y$ is the sum of their variances; i.e., $$\operatorname{Var}[X+Y] \overset{\text{ind}}{=} \operatorname{Var}[X] + \operatorname{Var}[Y],$$...
heropup's user avatar
  • 141k
1 vote

Volume under a normal distribution in cartesian and polar not integrating to 1

The $\sqrt{2\pi}$ you end up with is due to a missing factor in the denominator of the 2D density function. You should have integrated $$f_{X,Y}(x,y) = \frac1{\color{red}{2\pi \sigma^2}} \exp\left(-\...
user170231's user avatar
  • 20.6k
1 vote

Approximating a discrete distribution with CLT

If iid $Y_i\sim \text{Poisson}(\lambda)$ for $i=1,2,\dots,n$ and denote their average as $\bar{Y}$, then their sum $$ n\bar{Y}\sim \text{Poisson}(n\lambda) $$ exactly without approximation. Now if ...
Zack Fisher's user avatar

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