Recent content by user_01

I did not include the whole intermediate steps in the above solution which may cause confusion. Hence those steps are now presented below. --- **My solution** \begin{multline} \Phi = \mathbb{P}\left[ a\left(\frac{b}{1+\exp\left(-\bar \mu\frac{P_s X}{r^\alpha}+\varphi\right)}-1\right) \geq...

Given two i.i.d. random variables $X,Y$, such that $X\sim \exp(1), Y \sim \exp(1)$. I am looking for the probability $\Phi$. However, the analytical solution that I have got does not match with my simulation. I am presenting it here with the hope that someone with rectifies my mistake. ...

Is the following solution correct for the above question? If it is OK, then I have found the solution. But I will really appreciate if someone can let me know if the following method is correct. $$\mathbb{E}[g[x]] = \int_Q^\infty g(x). f(x) dx$$ $$\mathbb{E}[g[x]]=...

Given that $X$ is exponentially distributed continuous random variable $X\sim \exp(1)$ and $g(x)$ is as below. How can I find the Expectectaion of $g(x)$ for the condition that $x\geq Q$, i.e. $\mathbb{E}[g(x)\ | \ x\geq Q]$. $$g(x) = \frac{A}{\exp(-bQ+c)}\Big(\frac{1 + \exp(-bQ+c)}{1 +...

The following is the mathematical expression for my model's rate expression. Variables $x,y$ are the controlling parameter, while the rest are positive constants. $$\max_{x,y} \ ax + by^3 \ (s.t. \ 0\leq x \leq 1,\ 0\leq y\leq1)$$ Can I mathematically say that it is a convex problem within...