# Tag Info

Accepted

### Suppose I have 100 integers and I sample 10 without repetition. What is the expected rank of the lowest out of 10 samples?

To obtain an answer we must know how many ties there are among these $100$ integers and where they occur: that's too complicated and likely is not the intent of the question. (Nevertheless, the ...
Accepted

### Expectation of the ratio of sum (XY) and sum(X)

I will assume $a=0$ and $b=1$ in the following. Here is a simulation experiment to look at the variability of the expectation in $M$: ...

### Expectation of the ratio of sum (XY) and sum(X)

In your case of $\text{sum}(XY)/\text{sum}(X)$ you have that the $X$ and $Y$ are correlated. We can rewrite it in a different form such that we have a similar weighted average expression but with ...

### In a time series $x_t, x_{t-1},...,$, why is $E[x_t|x_t, x_{t-1},...]= x_t$?

As the comment by J. Delaney says, the result would hold even without conditioning on $x_{t-1}, x_{t-2},\cdots$. The statement in the OP's question might be the result of a bad cut-and-paste job from ...
Since the components are independent, it means that the squared $L_2$ norm of $\zeta$ has a $\chi^2_k$ distribution, which is the sum of squared independent standard normal variables. The expected ...