Questions tagged [median]

Question 1

I start with \$1. After one iteration of a game, one of the following $m$ outcomes occurs: With probability $p_1$, my wealth multiplies by $r_1$; With probability $p_2$, my wealth multiplies by $r_2$;...

Question 2

I'm currently analysing a binomial random walk which is given by $$\Delta\omega_t = \chi\left(\frac{W}{N} - \omega_t\right) + \eta_t\sqrt{\gamma}\ \omega_t$$ $$\omega_{t+1} = \omega_t + \Delta\omega_t$...

Question 3

Let $X_1,\dotsc,X_n$ be iid random variables with variance $\sigma^2 < \infty$. Let $M$ be the median of $X_1,\dotsc,X_n$. If it helps, assume that $n$ is odd (but more generally, I consider the ...

Question 4

I understand that the Wilcoxon Signed-Rank Test ranks the differences between the observed data and the assumed median, considering both the direction (positive/negative) and magnitude of the ...

Question 5

Given $n\ge 1$ triples $(x_1,y_1,z_1),\dots,(x_n,y_n,z_n)$ such that $x_i+y_i+z_i = 1$ and $x_i,y_i,z_i\ge 0$ for all $i$, we can compute their "extended median" as follows. Find a value $t$ ...

Question 6

For finding when the median of a beta distribution is $\frac{1}{2}$, this answer says: If a $\mathrm{Beta}(a,b)$ distribution has $a>b$ then $\mathbb P(X \le \frac12) \lt \frac12$ and its median ...

Question 7

Given five positive integer data $n_1,n_2,n_3,n_4,n_5$. Average of five data given is equal to 8. Now, we omitted two data and the average is equal to 6. Can we determine the range of median of five ...

Question 8

I am solving a problem involving a right triangle $ ABC$, where $ \angle A = 90^\circ $. The given conditions are shown in the image below: From the diagram, we are given: The angle bisector $ BL $ ...

Question 9

In the figure, $ABCD$ is a convex quadrilateral and E and F are respectively the midpoints of diagonals $AC$ and $BD$. Prove that: $$AB^2 + BC^2 + CD^2 + DA^2 = AC^2 + BD^2 + (4*EF^2)$$ (Hint: Use ...

Question 10

I have been stuck with the following problem for a while, maybe it will come as obvious to some of you. It states that there is some constant $C>0$ such that for any continuous logconcave density $...

Question 11

When using a Brute-force algorithm to calculate the Geometric Median, step by step, we are facing with a list a sums of distances. When we include, in the same list, a column with the number of ...

Question 12

I have two independent random variables $X$ and $Y$, where $Y$ is also independent of $Z$, and $E(X\mid Z=z)=0$ for any $z$. We also know that the conditional distribution of $X+Y$ given $Z=z$ is ...

Question 13

We have two independent random vectors $X$, $Y \in \mathbb{R}^d$ with the same distribution $F$. Is it then true that $$ \mathsf{P}\left( \left\langle X, Y \right\rangle \geq 0 \right) \geq 1/2? $$

Question 14

Let $X_j\overset{iid}\sim\mathrm{Unif}(-1,1)$. Let $\hat{X}_n$ be the sample median. What is the value of $n\mathbb E[\mathrm{sign}(X_1)\hat{X}_n]$ when $n\to\infty$?

Question 15

I recently stumbled on an algorithm while trying to write a program to estimate a median without sorting, a randomized group of non-repeating numbers with a known number of elements. Performance is ...

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Questions tagged [median]

Median wealth after repeated iterations of multiplicative game?

Analysis of a binomial random walk and calculating its median

Is the variance of the sample median of iid variables at most the variance of each variable?

Why does the Wilcoxon Signed-Rank Test consider the magnitude of differences when testing the median, rather than just the signs (positive/negative)?

Extended median of triples

Finding values that make the Beta function symmetric

Find median of five positive integer data

Finding the smaller leg and the median in a right triangle.

Prove the geometric relation in a convex quadrilateral with midpoints of diagonals

Bound on variance for logconcave density

Geometric median alternative definition, as maximum of distances less than the median-distance

Conditional median of $X+Y$ given $Z=z$

Is the median of an inner product of two i.i.d. random vectors non-negative? [closed]

Correlation of the median with the sign of an observation

I stumbled on a bruteforcing median algorithm. Can anyone tell me why it works and is there a name for this equation?

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