# Tagged Questions

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### Is there a name for sum over one set divided by the cardinality of another set?

What is the summation of one set real numbers divided by the cardinality of another set called? $$A \subset\mathbb R$$ $$\frac{\sum A}{|B|}$$ I will try and be specific to my problem because I lack ...
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### Expectations and variance with rolling a dice 10 times

Let's say you roll a fair dice 10 times and X is the number of sides that never show up. (i.e. Roll 1 - 10 = 1424145221, X = 2 because 3 and 6 never show up) Values of $N=0,1,2,3,4,5.\\ P(N=6) = 0$ ...
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### A small calculation .

How $\sum_{k=0}^n (-1)^n\times(-1)^{n-k}=\sum_{k=0}^n(-1)^k$ i got it $\sum_{k=0}^n(-1)^n\times(-1)^{n-k}=\sum_{k=0}^n(-1)^{2n-k}$ And is that $\mathbb E[\mathbb E(X)]=\mathbb E(X)$ ?
### How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$
How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$ i have tried to do that by the following procedure: $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2$ ...