Questions tagged [median]
For questions about the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.
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Median of a Poisson-Binomial distribution
Let $Z$ be a random variable following a Poisson-Binomial distribution with parameters $(p_1, \dots, p_n)$ such that $\sum_{i=1}^{n}p_i > \frac{n}{2}$. Consider the following two properties:
-If $n$...
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Number of possible histograms of a test given that the median is 60
There is the following problem I'm having a hard time coming up with a Sigma-less solution to:
If $360$ have taken a test, and grades can range from $0-100$ (inclusive), how many possible histograms ...
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Inequality with medians
It is well known that in any triangle $\triangle ABC$ with side lengths $a,b,c$ and medians $m_a,m_b,m_c$ inequality
\begin{equation}
\frac{3}{4}(a+b+c)<m_a+m_b+m_c<a+b+c
\end{equation}
holds. ...
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A possible error in a math question of 2022 Brazil's ENEM, a equivalent to US's SAT
This is a rather simple question, and it may seem like a physics question, but it actually belongs to a math test. I'll translate it into English first and then reproduce the Portuguese version.
"...
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Median of Mixed Random Variable [closed]
I have the following CDF
$$
F_X(x) = \begin{cases}
0 & x < 0 \\
1 - p e^{-x} & x \geq 0
\end{cases}
$$
I found $\mathcal{X} = \{ 0\} \hspace{0.1cm} \cup (0,\infty)$ with $P(X = 0) = 1-p$ ...
- 753
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Finding the distribution of the median of three independent random variables
Problem:
Let $Y_1$, $Y_2$ and $Y_3$ be independent and uniformly distributed over the
interval $(0,1)$. Let $Y_0$ be the median of the three variables. Find the probability density for $Y_0$.
Answer:
...
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Medians from rows of numbers
You have three rows of numbers, $(a_1,a_2,a_3), (b_1,b_2,b_3), (c_1,c_2,c_3)$, each in the range $[0,1]$ and summing up to $1$. If the medians of the three columns are $m_1,m_2,m_3$ with sum $m$, you ...
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The Medians of Lipschitz Functions on $(X,d,\mu)$ (Existence and Uniqueness)
Let $\varphi:(X,d,\mu)\to \Bbb R$ be a Lipschitz function, where $\mu$ is a probability measure on the metric space $(X,d)$. The median $m_\varphi$ of $\varphi$ is defined as the real number such that
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median of multivariate Gaussian
I have the following basic question. I am interested in the spatial median of mutlivariate Gaussian random variable. Let $d$ be the dimension and let $\mathcal{N}(\mu,I_d)$ denote the multivariate ...
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Finding the median value, am I missing something?
If I'm not missing anything, please tell me. This is my understanding of the definition of a statistical mean:
Using the definition: The median is the middle value that separates the lower and higher ...
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Maximum Likelihood Estimation of median for an exponential distribution
Given data x1, ... xn i.i.d. with exponential distribution and unknown parameter λ, determine maximum likelihood estimation of θ given the observed data where theta is the median of the distribution.
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What is the probability that a subset of size $m$ will have the same median as the set of size $n$?
I feel like I have been bashing my head against the wall on something that I thought would be easy. Not from a math background so this might actually be trivial.
I have a set of numbers $S$ with size $...
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Why I am getting two different medians
let's say we have: $10, 12, 15, 10, 10, 12$
sorted: $10,10,10,12,12,15$
this way is clear that the median is $\frac{10+12}{2} = 11$
however, I was told that I could find the median using this table
...
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Is the median a measurable function of the probability distribution?
For $\mu \in \mathcal P(\mathbb R)$, let $m(\mu)$ be the median of $\mu$, defined as the smallest of all medians of $\mu$ as follows:
$$
m(\mu) = \inf \left\{ x \in \mathbb R \,\middle|\, \mu((-\infty,...
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Distance of a hyperplane from Geometric Median
Let $d,n \in \mathbb{N}$. Assume we have $n$ points, $x_1,\dots,x_n$ where for every $i \in \{1,\dots,n\}$, we have $x_i \in \mathbb{R}^d$. Define the geometric median as
$$
\theta^\star \in \arg\min_{...
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