Intereting Posts

Evaluating $\int_{I^n} \left( \min_{1\le i \le n}x_i \right)^{\alpha}\,\, dx$
Is the hyperbola isomorphic to the circle?
Probability to choose specific item in a “weighted sampling without replacement” experiment
VC dimension for Rotatable Rectangles
Derangements with repetitive numbers
Shortest and most elementary proof that the product of an $n$-column and an $n$-row has determinant $0$
How do iterative methods applied to the companion matrix of a polynomial $p(\lambda)$ relate to $p$ itself?
A curious identity on sums of secants
Is there a faster way to do this? Find an orthogonal matrix $P$ and a diagonal matrix $D$ such that $A=PDP^T$
Continuity of the Ito integral
determine the closures of the set k={1/n| n is a positive integer}
The $n^{th}$ root of the geometric mean of binomial coefficients.
Union, intersection, set theoretic difference of recursively enumerable sets
What is finite in a finite model
Fundamental group of the complement of Borromean rings

Let $f(x)$ and $g(x)$ be two probability density functions. Does the expression:

$$

C = 2\int _{-\infty}^{\infty}\left[f(x)\int _{-\infty}^{x}g(y)\,dy\right]\,dx

$$

have any meaningful graphical representation when $E[Y]>E[X]$, where $X$ has $pdf$ $f(x)$ and $Y$ has $pdf$ $g(x)$? Or, can it be expressed in a simpler fashion?

- Probability that the bag contains all balls white given that two balls are white
- Generalizing the total probability of simultaneous occurrences for independent events
- Universal algorithm to estimate probability of drawing certain combination of coloured balls
- n tasks assigned to n computers, what is the EX value of a computer getting 5 or more tasks?
- How does scaling $\Pr(B|A)$ with $\Pr(A)$ mean multiplying them together?
- Let $\{X(t)\}$ be a Poisson process with arrival rate $\lambda>0$. Compute the conditional probability, $P(X(s) = x|X(t) = n)$.

From some numerical simulations, it seems to approximately describe the “overlap” area of the two $pdf$’s. And if we let $g(x)==f(x)$ then $C$ is close to 1…

The overlap is defined as,

$$\int_{-\infty}^{\infty} \min(f(x),g(x)) dx $$

- Variance of a stochastic process with Gaussian correlation function
- It's a complicated case of simple dice roll.
- Bound variance proxy of a subGaussian random variable by its variance
- Monte-Carlo simulation with sampling from uniform distribution
- Probability of getting two pair in poker
- Help with a Probability Proof
- Expected number of tosses for two coins to achieve the same outcome for five consecutive flips
- Expected Number of Coin Tosses to Get Five Consecutive Heads
- Distribution for random harmonic series
- Given n ranging from 1 to 100, find sum of digits equal to half of arithmetic sum of 1 to 100

If $X$ and $Y$ are independent continuous random variables with densities $f(x)$ and $g(y)$ then the probability that $Y$ is less than or equal to $X$ is

$$\Pr (Y \le X) = \int _{x=-\infty}^{\infty}[f(x)\int _{y=-\infty}^{x}g(y)dy]dx$$ and graphically is the probability of being below the line $y=x$.

$C$ is twice this. If $g(x)=f(x)$ for all $x$ then it is the probability of being above or below the line and (ignoring the zero measure of being on the line) is $1$.

- Bringing ordinals to standard polynomial form
- Least-upper-bound property Rudin book
- Seeking proof for the formula relating Pi with its convergents
- Jordan canonical form of an upper triangular matrix
- $f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
- Proving the inequality $4\ge a^2b+b^2c+c^2a+abc$
- Definition of a monoid: clarification needed
- Book on combinatorial identities
- How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}…}}}}=2$
- A Bernoulli number identity and evaluating $\zeta$ at even integers
- The determinant of block triangular matrix as product of determinants of diagonal blocks
- Local coefficients involved in the obstruction class for a lift of a map
- What's are all the prime elements in Gaussian integers $\mathbb{Z}$
- Proving the triangle inequality for the $l_2$ norm $\|x\|_2 = \sqrt{x_1^2+x_2^2+\cdots+x_n^2}$
- Extend isometry on some cube vertices to the entire cube