Intereting Posts

Conditional Expectation of a Poisson Random Variable
How does the axiom schema of replacement work?
Evaluating $\int_0^1 \frac{x \arctan x \log \left( 1-x^2\right)}{1+x^2}dx$
On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
What is the intuition behind the unit normal vector being the derivative of the unit tangent vector?
Why is the supremum of the empty set $-\infty$ and the infimum $\infty$?
Galois' theorem that $|F|=p^n$
Flipping coins in a chessboard
Suppose $f : \mapsto R$ is continuous, $f$ is differentiable on $(0,1) $and $f(0)=0$.
Proving that $\int_0^1 \frac{\log \left(\frac{1}{t}\right) \log (t+2)}{t+1} \, dt=\frac{13}{24} \zeta (3)$
Why $X$ independent from $(Y,Z)$ implies that $E(XY^{-1} | Z)= E(X) E(Y^{-1}|Z)$?
Is there a geometric meaning to the outer product of two vectors?
Clairaut's Theorem And continuity of a multivariate function
Finding a prime number $p$ and $x, y, z\in \mathbb N$ such that $x^p+y^p=p^z$
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$

Why is $\sum_{k=0}^n (_k^n) 2^k$ simplified as $3^n$ and not just $2^n$ ?

The answer uses the binomial theorem as a solution: let $a=1$ and let $b=2$. So $1+2 = 3$. But since $1+2 = 3$ why do we not use $1+1 = 2$?

- There are $6$ types of cookies. How many different packs of $3$ cookies can the baker package?
- Numbers fulfilling a certain condition in a range of numbers
- Give a Combinatorial proof to show $\sum_{i=1}^{n}{iC(n,i)}=n2^{n-1}$
- Distinct digits in a combination of 6 digits
- A binary sequence graph
- How many ways can you pick out 15 candies total to throw unordered into a bag and take home
- Combinations problem involving a standard pack of $52$ playing cards and a $4$ sided die: Part 1
- Probability of two people meeting in a given square grid.
- What is the probability that if five hats are distributed among five boxes that box $B_1$ has hat $H_1$ or hat $H_2$ but not both?
- Dealing a 5 card hand with exactly 1 pair

It is $$\sum_{k=0}^n \binom{n}{k} 2^k \cdot 1^{n-k}=(1+2)^n$$

- Proving that $T_t := S_t -\left| x \right| -\frac {n-1}{2} \int _0 ^t \frac {1}{S_u}~du$ is a brownian motion
- Always a double root between “no roots” and “at least one root”?
- Explain Zermelo–Fraenkel set theory in layman terms
- topologies of spaces in escher games
- Proof that $\Bbb Z$ has no other subring than itself
- Compact Lie group bi-invariant metric
- Do “imaginary” and “complex” angles exist?
- Uniqueness of curve of minimal length in a closed $X\subset \mathbb R^2$
- finding code of a function in GAP packages
- Jordan normal form and invertible matrix of generalized eigenvectors proof
- In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
- Help me prove equivalently of regular semigroup and group.
- Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
- What in Mathematics cannot be described within set theory?
- “Proof” that $\mathbb{R}^J$ is not normal when $J$ is uncountable