Intereting Posts

One divided by Infinity?
Looking for Cantor's original proof of the Cantor-Bernstein theorem that relies on the axiom of choice?
Solving infinite sums with primes.
Unions and Intersections of Open Sets are Open
Bubble sorting question
Different standards for writing down logical quantifiers in a formal way
Condition on degrees for existence of a tree
Solving the recurrence $t(n)=(t(n-1))^2 + 1$
Understanding direct sum of matrices
Show that $1^k+2^k+…+n^k$ is $O (n^{k+1})$.
Covering of a topological group is a topological group
Show that $\sum\limits_{i=0}^{n/2} {n-i\choose i}2^i = \frac13(2^{n+1}+(-1)^n)$
Distance between two points on the Clifford torus
Derived sets – prove $(A \cup B)' = A' \cup B'$
A Pick Lemma like problem

I have a question. Let’s suppose that the two random variables $X1$ and $X2$ follow two Uniform distributions that are independent but have different parameters:

$X1 \sim Uniform(l1, u1)$

$X2 \sim Uniform(l2,u2)$

- Why is Binomial Probability used here?
- Deal or no deal: does one switch (to avoid a goat)?/ Should deal or no deal be 10 minutes shorter?
- Improper Random Variables
- Largest Part of a Random Weak Composition
- Probability from a collection of independent predictions
- Find thickness of a coin

If we define X3 as the maximum of X1, and X2, i.e., $X3 = max(X1, X2)$, what kind of distribution would it be? It is certainly not a uniform and I can calculate the cumulative probability, i.e., $p(X3 <= a)$, because $p(X3 <= a) = p(X1 <= a) p(X2 <= a)$. But, I wonder if there exists any density function that can model X3.

- Probability of having at least $K$ consecutive zeros in a sequence of $0$s and $1$s
- probability of three random points inside a circle forming a right angle triangle
- Seating of $n$ people with tickets into $n+k$ chairs with 1st person taking a random seat
- Joint probability distribution (over unit circle)
- Better than random
- A question about Poker (and probability in general)
- Simulating uniformly on $S^1=\{x \in \mathbb{R}^n \mid \|x\|_1=1\}$
- Proof of “continuity from above” and “continuity from below” from the axioms of probability
- What is the probability of the sum of four dice being 22?
- Jensen's Inequality (with probability one)

The distribution of $Z = \max(X,Y)$ of independent random variables is

$$F_Z(z) = P\{\max(X,Y)\leq z\}

= P\{X \leq z, Y \leq z\} = P\{X\leq z\}P\{Y \leq z\} = F_X(z)F_y(z)$$

and so the density is

$$f_Z(z) = \frac{d}{dz}F_Z(z) = f_X(z)F_Y(z) + F_X(z)f_Y(z).$$

All of this holds regardless of the distributions of $X$ and $Y$, that is,

they need not be uniformly distributed random variables. But, for

uniform distributions, the density of $Z$ has simple form since $f_X(z)$ and

$f_Y(z)$ are constants and $F_X(z)$ and $F_Y(z)$ are constants or linearly

increasing functions of $z$. For example, if $X, Y \sim U(0,1)$, then

$f_Z(z) = 2z$ for $0 < z < 1$.

- Significance of the Riemann hypothesis to algebraic number theory?
- Definition of group action
- “This property is local on” : properties of morphisms of $S$-schemes
- Basis of a $2 \times 2$ matrix with trace $0$
- Non-additive asymptotic upper density: $\mathsf{d}^\star(A\cup B) \neq \mathsf{d}^\star(A)+\mathsf{d}^\star(B)$
- Would a proof to the Riemann Hypothesis affect security?
- Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
- If $(y_{2n}-y_n) \to 0$ then $\lim_{n\to \infty} y_n$ exists
- How to prove that $L^p $ isn't induced by an inner product? for $p\neq 2$
- Three points on sides of equilateral triangle
- What is a support function: $\sup_{z \in K} \langle z, x \rangle$?
- Find pairs of side integers for a given hypothenuse number so it is Pythagorean Triple
- inverse element in a field of sets
- Is a differentiable function always continuous?
- Simplifying a certain polylogarithmic sum in two variables