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Finding the Moment Generating function of a Binomial Distribution
Suppose $X$ has a $\rm{Binomial}(n,p)$ distribution. Then its moment generating function is \begin{align} M(t) &= \sum_{x=0}^x e^{xt}{n \choose x}p^x(...
Apr 21, 2026
Archive: News
![Analytic vs. Analytical [closed]](https://news.conceivablytech.com/uploads/analytic-vs-analytical-closed_720.jpg)
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Analytic vs. Analytical [closed]
I am trying write an article. Little Summary: I have developed some tools to analyze derivative of some function $f$. This characterization leads to bette...
Apr 21, 2026
news
What does the cross product of the velocity and position vector represent?
This is a theorem from my text: First, why are we taking the cross product of the position and velocity vectors? What is the physical representation of th...
Apr 21, 2026
news
Collatz conjecture but with $\ 3n-1\ $ instead of $\ 3n+1.\ $ Do any sequences go off to $\ +\infty\ $?
Collatz conjecture but with $\ 3n-1\ $ instead of $\ 3n+1.\ $ Do any sequences go off to $\ +\infty\ $? $$$$ Background (not necessary to answer my questi...
Apr 21, 2026
![How to proof the the derivative of $x^2$ is $2x$? [closed]](https://news.conceivablytech.com/uploads/how-to-proof-the-the-derivative-of-x-2-is-2x-closed_720.jpg)
news
How to proof the the derivative of $x^2$ is $2x$? [closed]
I need your help, my question is how to proof that the derivative of $x^2$ is $2x$? Please I need a clear explanation.
Apr 21, 2026
![What is the value of $i^i$? [duplicate]](https://news.conceivablytech.com/uploads/what-is-the-value-of-i-i-duplicate_720.jpg)
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What is the value of $i^i$? [duplicate]
I understand that when you raise any number $x$ to a power, you multiply $x$ by itself the number of times indicated in the power. However, what happens w...
Apr 21, 2026
news
Finite automaton that recognizes the empty language $\emptyset$
Since the language $L = \emptyset$ is regular, there must be a finite automaton that recognizes it. However, I'm not exactly sure how one would be co...
Apr 21, 2026
news
Length of line segment in diagram
Question: Consider the diagram below. How can one express the length of $z$ in terms of $a$, $b$, and $c$ without including $x$ in the expression? If it i...
Apr 21, 2026
news
Restrictions of compositions
Considering two functions, $f,g:X\to X$ s.t. $Y\subseteq X$ is invariant for both $f$ and $g$, that is $f(Y)\subseteq Y$ and similar for $g$. Do we then h...
Apr 21, 2026
news
Optimal Degenerate Basic Feasible Solution with Positive Reduced Cost
For a standard form linear program that minimizes an objective function as follows: $$ \begin{aligned} \text{minimize } &c^T x \\ \text{subject to } &...
Apr 21, 2026
