All Questions
4 questions
8
votes
1
answer
12k
views
Variance and expectation of dot product
I am wondering what is the $E[\textbf{a}\cdot \textbf{b}]$ and $var[\textbf{a}\cdot \textbf{b}]$
where $\textbf{a}, \textbf{b}$ are independent random vectors. That is as a vector whose elements are ...
- 103
3
votes
3
answers
3k
views
Expectation of a square root of a sample mean
Let $X_i$ be iid exponential random variables. I want to calculate $Var\left(\sqrt{\bar{X}/6}\right).$
The idea I had to simplify this is expressing it as $$Var\left(\sqrt{\frac{\bar{X}}{6}}\right) =...
- 802
0
votes
0
answers
833
views
Joint Density and Covariance between Two Random Variables with the same Mean and Variance
This seems like a deceptively simple question, (and it perhaps is and I am missing something) but I could not find anything on this.
Q1)
Are there any general results / relationships to get the Joint ...
- 385
0
votes
0
answers
77
views
Is the inverse of the sample variance integrable?
Is the inverse of the sample variance integrable? That is, does it hold that
$$
E\bigg[\bigg(\frac{1}{n}\sum_{i=1}^n X_i^2 - \overline{X}_n^2\bigg)^{-1}\ \bigg] < \infty.
$$
- 893