1
vote
2answers
43 views

What is the distribution of the average of IID exponential RVs? (have to use MGFs)

Just a quick question as I cannot figure this out. Here is the problem: Q: What is the distribution of the following? ($Y_1 + Y_2 + Y_3 +\cdots+ Y_n$) $ /n$ if each $Y$ is independent and identically ...
2
votes
1answer
47 views

Median and Mean of Sum of Two Exponentials

I have a cumulative distribution function: $$G(x) = -ae^{-xb} - ce^{-xd}+h$$ The associated probability density function is: $$g(x) = abe^{-xb} + cde^{-xd}$$ My problem concerns $x\ge 0, X \in R$. I ...
0
votes
0answers
34 views

Formula for roots on an arbitrary polynomial

This question is related to a previous question I have posted: Solution for a Mixture of Two Exponential Equations I have reduced my problem to the following equation: $\left( ...
4
votes
1answer
346 views

sum of $\displaystyle \frac{\sin nx }{n^4}$

Consider : $\displaystyle f(x)= \sum_{n=1}^{\infty} \frac{\sin nx }{n^4}$ Find : $\displaystyle \int_0^{x} f(t)\ \mathrm{d}t$.
0
votes
1answer
108 views

A hard limit with integral sign

$$\displaystyle\underset{m\to +\infty }{\mathop{\lim }}\,\left[ \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\int_{0}^{x}{{{\left( \underset{n\to \infty }{\mathop{\lim }}\,{{\left( 1-\frac{1}{n} ...
1
vote
3answers
367 views

Summing a exponential series

What is the appropriate way to simplify such an expression. i am unsure of how to use the series i know to apply to this situation $$\sum_{L=0}^{M}s^{L}L^{2}$$ do i modify such a series as power ...