1
vote
1answer
67 views

Limit of characteristic function

I have a characteristic function defined as the following: $$\phi(\frac{t}{N})^N = (\alpha E_{\alpha+1}(-\frac{iLt}{N}))^N$$ where $E_n(z)$ is the $E_n$ function having the form $E_n(z) = ...
2
votes
2answers
126 views

Finding a definite integral by residue integration?

I have a probability distribution of the form $$\frac{k_1}{(k_2 x^2+k_3 x+k_4)^n}$$ and I want to find the mean and variance—but am running into problems with that. The mean would be ...
4
votes
2answers
296 views

The law of large numbers: How does the convergence take place? How does the “remainder” look like?

I have the independent and identically distributed random variables $X_1,X_2,\ldots$ with a finite expectation $\mu$. I also have defined $S_n = X_1 + \cdots + X_n$. According to the law of large ...