Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
2
votes
1 answer

Interpolation needed

I have a series of datasets which I need to interpolate, I did this once in uni but that was a long time ago. I could use any pointers I can get. So I have put the data up here in the hope that someone might be able to explain to me how I may…
klonq
  • 133
2
votes
2 answers

Sufficient Statistics, MLE and Unbiased Estimators of Uniform Type Distribution

Let $X_1, \dots, X_n$ denote a random sample of size $n$ from the probability distribution with pdf: $$ f_X(x\mid\theta_1, \theta_2) = \frac{1}{\theta_2 - \theta_1} \ I(x)_{[\theta_1,\theta_2]} \ I(\theta_1)_{(-\infty,\theta_2)} \…
user45185
  • 277
2
votes
1 answer

Scaling vector with multivariate normal

If I have a vector $\mathbf{\bar{X}}=\frac{1}{N}\sum_{i=1}^N \mathbf{X}_i$ such that it is known by CLT that $\sqrt{N}(\mathbf{\bar{X}}-\bar{\mu})$ (here $\bar{\mu}$ is the mean vector) converges in distribution to a multivariate normal…
fejz1234
  • 542
2
votes
1 answer

Find $\lambda $ such that P(X=1)=$\frac{1}{2}$ where X is Poisson($\lambda$)

Find $\lambda $ such that P(X=1)=$\frac{1}{2}$ where X is Poisson($\lambda$). Using the formula $P\left(X=x\right)=\frac{\lambda^xe^{-\lambda}}{x!}$ and plugging in 1 for x I was able to simplify it down to $\lambda e^{-\lambda}=\frac{1}{2}$. I was…
Micah Ludwick
  • 33
2
votes
0 answers

How do you compare data values that come from different data sets using standard deviation?

My textbook had this question: "Two swimmers, Angie and Beth, from different teams, wanted to find out who had the fastest time for the 50 meter freestyle when compared to her team. Which swimmer had the fastest time when compared to her…
Joe
  • 485
2
votes
1 answer

Why couldn't we use x / average for standardization instead of z scores?

As I was reviewing data standardization and z score theory, i had this intuition. Suppose you have the results of people who took two different tests: TEST A (mean=70%; std.dev=6%) +--------------+-------+---------+-------+ | Participant# | score |…
Vincent Labrecque
  • 121
2
votes
2 answers

Assigning a value to how 'ordered' a vector is

Consider a vector which goes in ascending order from (1, 2, 3 ... N). This vector is ordered 'correctly' and I would like to assign it a score of 1, which indicates a perfectly ascending ordered vector. On the other hand, a vector (N, N-1, N-2 ...…
Rachel
  • 23
2
votes
1 answer

Collisions during random insertion unto given domain

Here's a satisfying one. Assume a list of maximum length L which starts out empty. For the first element we pick a random number within the domain [0 ... L), we check if the list already contains it (it obviously doesn't when the list is empty), and…
Bogdan Stăncescu
  • 161
2
votes
1 answer

Determining the distribution of a population from a sample

I have a uniformly collected sample of 10000 data points from a population of about 200000. I'd like to find out what the distribution of the population is. How can I do this rigourously?
Undercover Mathematician
  • 314
2
votes
1 answer

How many possibilities can a 10x5 grid with somewhat even distribution produce?

Imagine a 10 x 5 grid where each square can be either 1 or 0. However, each row (10 squares) must contain five 1's and five 0's. Therefore, each grid (of 50 squares) has twenty five 1's and twenty five 0's but their distribution is somewhat…
lurning too koad
  • 127
2
votes
4 answers

Proof $X_n\xrightarrow{D}X$ and $Y_n \xrightarrow{P}0$ then $X_n + Y_n \xrightarrow{D}X$

I am having trouble proving this theorem. I know that I am given $$\lim_{n \rightarrow \infty }Pr[X_n \epsilon] = 0, \quad\forall\epsilon>0$$ where I have to show that $$\lim_{n…
hyg17
  • 5,117
  • 4
  • 38
  • 78
2
votes
1 answer

Scaling a uniform distribution - Probability

I just have a simple question on scaling a uniform distribution. I know that uniform distribution has probability density of $1/(b-a)$ defined on the interval a to b. My textbook says that we can scale the distribution to be between (0,1) and have…
Zhulu
  • 1,259
2
votes
0 answers

How to find the mean squared error in an exponential distribution?

Say we are given an exponential distribution. This questions first asks you to find the MLE of $\theta$ an exponential distribution which I found to be equal to $\bar{X}$. Then it asks you to compute the Mean Squared Error? I have no idea how to do…
George Harrison
  • 457
  • 3
  • 7
  • 13
2
votes
2 answers

Can probabilities sometimes add to greater than one?

I read on my textbook that in a certain scenario, the sum of the probabilities is supposed to equal to one. However, I read an example of an event on this site, and it says in some cases, independent events can add to greater than one. For example,…
chris
  • 35
2
votes
1 answer

A Problem about Hypothesis Testing and Decision Making

I have a problem about the hypothesis testing and decision making as follows: A botanist wishes to test the null hypothesis that the average diameter of the flowers of a particular plant is 9.6cm. He decides to take a random sample of size $n$=80…
Scorpio19891119
  • 2,345
1 2 3
…
99 100