# Tagged Questions

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### Just learned about the bell curve in statistics. How is calculus related to this curve?

I'm learning about the bell curve in statistics and I'm trying to understand the calculus behind the concept. I've taken calc 1 already. How is the integral related to this ...
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### If a random variable X has mean of μ and standard deviation σ…

, then what will be the mean and standard deviation of (X − μ)/σ ?
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### if $X_i$ are iid standard normal distributed, what is the limiting distribution of $\sum X^4 / (\sum X^2)^2$?

If $X_i$, $i=1,\ldots,n$ are iid standard normal distributed, what is the limiting distribution of $S_n=\sum X^4 / (\sum X^2)^2$? After finding the moments and since $Cov(X^4, X^2)=0$, I have the ...
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### Given N-distribution, calculate expected value and Var of a function

$X_{{i}}=X_{{1}}...X_{{n}}$ is an iid. random variable with the distribution $N \left( {\frac {\alpha}{\beta}},{\frac {{\alpha}^{4}}{{\beta}^{4}}} \right)$ I would like to calculate the expectation ...
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### Finding probability density function of a linear combination of mutually independent normal random variables

I'm finding the probability density function of the random variable U defined in the following manner: $$U=\frac{1}{2}(Y_1+3Y_2)$$ CORRECTION: The line above is supposed to be ...
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### Intuition and the math behind normalization

What exactly is the purpose of normalization. From what I read, it is to adjust two different sets of values so you can compare them, but I don't understand why, nor the math behind it. Could anyone ...
### If $X \sim N(0,1)$, why is $E(X^2)=1$?
If $X$ is a normally distributed with mean $0$ and variance $1$, expectation of $X$ equals $0$ but why is $E(X^2)=1$?
Part 1 Let $X$ be a random variable with the p.d.f. $f(x)=\frac{1}{4\pi}e^{\frac{-x^2}{4}}$, compute the MGF of $X$. So I know I want ...