I know how to fit a curve when given some data points in the cartesian coordinate. Recently, I encountered a model that needs to fit a closed curve in the polar coordinate. I’m thinking of deducing a similar formula using Maximum Likelyhood, but the problem is I don’t know what kind of hypothesis to choose. […]

A lot of questions about the birthday problem can be found here, but none seems to address my problem: Background I am thinking of a hash-type data structure design which accepts a certain number of collisions to occur. Collisions shall be detected and handled in a second data structure with substantially lower collision probabilities. The […]

It can be shown that VC dimension of rotatable rectangles is 7. The problem is I cannot understand how to approach the solution. So far I used bruteforce to solve this kind of problem, I was drawing points in different shapes and check whenever the hypothesis shatters the points. In this case the heptagon is […]

What is the probability density function of the following product of uniformly distributed random variables: $Y=X_1\dotsb X_n$, where $X_n \thicksim U[1,2]$ (Uniform distribution); the $X_n$ are independent. OBS: It is not a duplicate. I found the answer only for the $U[0,1]$ and here, there is no analytical equation for the pdf.

Consider a random sample $X_{1}, \dots, X_{n}$ where $X \sim \mathrm{unif}[0, \theta]$ for $\theta \in (0, \infty)$. Usually we prove that $T = X_{(n)}$ is a sufficient statistic for $\theta$ by appeal to Neyman’s Factorization Thoerem. I’d be interested in demonstrating the sufficiency of $T$ by showing that the conditional distribution $X\mid T$ does not […]

Let’s say I don’t know how many days there are in a year (N) and want to figure this out by asking people for their birthday. I ask D random people for their birthday and find there are E duplicate birthdays. How can I estimate N? For example, say I draw: 24, 49, 52, 28, […]

I want to test if two samples are drawn from the same distribution. I generated two random arrays and used a python function to derive the KS statistic $D$ and the two-tailed p-value $P$: >>> import numpy as np >>> from scipy import stats >>> a=np.random.random_integers(1,9,4) >>> a array([3, 7, 4, 3]) >>> b=np.random.random_integers(1,9,5) >>> […]

My question is: do you know any examples when $X$ and $Y$ are both normally distributed, but the two dimensional vector $(X,Y)$ is not? I found some example in book, but I don’t understand it. The example is: Let us assume that $f_1$ and $f_2$ are both the densities of $2D$ normal distribution with $0$ […]

Is there a way to update a normal distribution when given new data points without knowing the original data points? What is the minimum information that would need to be known? For example, if I know the mean, standard deviation, and the number of original data points, but not the values of those points themselves, […]

I am trying to show that a normal distribution with parameters $\mu = 0$ and variance $\theta$ is not complete. I am looking for a function $u(x)$ that is not equal to 0 such that $\mathbb E(u(x)) = 0$. I have done some research on this problem and I have found that $\bar{X}$ and $S$ […]

Intereting Posts

Studying mathematics efficiently
Symmetric monoidal products that preserve limits and colimits
local convexity of $L_p$ spaces
how to show convergence in probability imply convergence a.s. in this case?
Converging series in Banach space
Proving formula involving Euler's totient function
For bounded sequences, does convergence of the Abel means imply that for the Cesàro means?
Why is $\pi$ so close to $3$?
Prime Numbers and a Two-Player Game
When does the two cars meet
Spectrum of the sum of two commuting matrices
What is the exact definition of a reflexive relation?
Evaluation of the integral $\int_0^1 \log{\Gamma(x+1)}\mathrm dx$
Find a basis given a vector space
What mathematical structure models arithmetic with physical units?