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2

Based on the comments above with credits to Gregg H, for this example the required amount of burgers are computed as, $$32\left(1.05 + \dfrac{2.576(\sqrt{0.4475})}{\sqrt{32}}\right) = 43.348... \rightarrow 44$$ Where the term in the brackets is the upper-bound for the CI (at 99%) for the expected burgers to be had by one person. This happens to be a ...

2

I think you are operating under some misapprehensions here. Firstly, we estimate unknown things from the data we have, not from data we might have gotten instead. Every statistical estimator is a function that maps all possible data vectors we can observe to the space of possible values of the thing we are estimating --- we obtain the estimate by ...

-1

This is sometimes called the 'CLT for medians'. Similar, limiting distributions hold for quantiles other than the median (but not for the maximum or minimum). As you say, the condition for the CLT for means, is that the population have finite variance. By contrast, the key condition that assures convergence of sample medians to normal is that the value of ...

6

I think you're confusing the Lebesgue integral with Itô calculus. They are related concepts. I'll explain. Lebesgue vs Riemann The simplest explanation of the difference between Lebesgue and Riemann integration - that I know of - follows. Imagine a bunch of bank notes tossed on a carpet. Riemann would count the money by first drawing a rectangular grid on a ...

0

If you want to know if there is a significant difference in the "before" and "after", then you probably should do a Paired t-test. These tests are done when the same individuals are measured twice. When you perform the Paired t-test, you choose the significance level that you want and then you check the p-value obtained from the test. If ...

4

For simplicity, assume $m=0$ and odd $n=2r+1$. The pdf of $Y_n$ is $$f_n(y)={n\choose r} f(y) F(y)^r(1-F(y))^r$$ and we are interested in whether $\int y^2f_n(y)\,dy$ exists. We know $F(y)\to 0$ as $y\to-\infty$ and $1-F(y)\to 0$ as $y\to\infty$. If $F$ approaches 0/1 at some polynomial rate, then some power $r$ will approach faster than $y^{-2}$, ...

1

The difficulty disappears when you are careful in formulating the limits. In the first case, $p$ is not constant, so it would be more precise to write it as $p_n$, as $p$ varies with $n$. We can write $n \cdot p_n \to \lambda>0$ another way as $p_n \sim \lambda/n$, where $\sim$ means that the quotient between the two sides converges to unity with \$n \to\...

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