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

A question about $\sum_{i=1}^n x_i x_i^T = X^TX$

For a set of column vectors $x_1,\dots,x_n$, the identity shows that $\sum_{i=1}^n x_i x_i^T = X^TX$. I can show this by seeing the $(p,q)$ entry of the resulting matrix is $\sum_{i=1}^n (X^T)_{pi}X_{iq} = \sum_{i=1}^n x_{ip} x_{iq}$. Is there a…
David Tan
  • 745
2
votes
1 answer

How do I weight Win/Loss Percentage Based on Games Played?

I have a spreadsheet I use for tracking my statistics in a game across a number of different factors such as Map, Group Size and Class. In each case, I use the win percentage to determine a rating out of 5 (rounded to the nearest $.01$). For…
Declan Murphy
  • 23
  • 3
2
votes
2 answers

Statistics Homework Question (Binomial Distribution)

Problem: In a binomial experiment with 45 trials, the probability of more than 25 successes can be approximated by $P(z > \frac{(25-27)}{3.29}$) What is the probability of success of a single trial of this experiment? Choices:…
bandicoot12
  • 397
2
votes
1 answer

What is the prob that the seq obtained is inc (ie. nondecreasing)

Given n distinct numbers, k numbers are picked out, 1 by 1 w/ replacement to get a seq of numbers. What is the prob that this seq is increasing? I know that since non-decreasing seq are allowed, there are in addition n constant seq on top of the…
cloudwalker
  • 21
  • 2
2
votes
1 answer

Why is my Cauchy Distribution going way larger than 1?

I believe my answer to be simple but I will explain as I cannot figure it out. I am writing a simulation for an optical experiment. I have a very small square plate target of dimentions $W \times W$. I want to set up a laser linewidth that has a…
user41178
  • 234
2
votes
1 answer

Transform normal distribution to chi-square distribution

Let $X_1$ and $X_2$ be independent random variables with distributions, with $X_1 \sim N(-1; 2)$ and $X_2 \sim N(2; 3)$ Prove that random variable $Y_2=((2X_1+X_2)^2)/11$ is chi-square distributed. My approach: $2X_1+X_2 =Z,$ with $Z \sim…
user430953
  • 153
2
votes
3 answers

The Poker Hand or Don't Call Out the Professor

This goes back to a problem given to my statistics class, 50 years ago. You are dealt 5 cards from a standard deck of 52. What are the odds of you having the Queen of Spades? The Professor said to work on it and be prepared to answer the following…
John Richard
  • 21
  • 1
2
votes
1 answer

PDF of a ratio of functions of order statistics

Question: Let $X_1,\dots,X_n$ be iid from a distribution with cdf $F(\cdot)$. Find the pdf of $\dfrac{1-F(X_{(2)})}{1-F(X_{(1)})}$. I know that $F(X) \sim \mathcal{U}(0,1)$ for any r.v. $X$, so in this case, we're looking for the pdf of $\dfrac{1-…
user365239
  • 1,988
2
votes
0 answers

Prove formula for expected value for exponential families

Let $\{P_\theta: \Theta \subset \mathbb{R^k}\}$ be a regular statistical family. Let $T=(T_1,\ldots,T_k)$ has density of form: $\displaystyle f=c(\theta)\cdot h(t) \cdot \exp \left\{\sum_{j=1}^{k}\theta_jt_j\right\} $. Let $\ell_1\ge0, \ldots ,…
Mario
  • 559
2
votes
0 answers

How to calculate covariance and correlation?

Consider for $c\in \mathbb R $ the function $f:\mathbb R→\mathbb R$ is defined by $$f(t)=\begin{cases} c(t-1), & 1 \leq t <2\\ c, & 2 \leq t <5 \\ \frac{-c}{2}(t-7), & 5 \leq t <7 \\ 0, & \text{otherwise} \end{cases} $$ By choosing the appropriate…
Ana Matijanovic
  • 1,325
2
votes
1 answer

Proving that a MLE is an asymptotically unbiased estimator

Let $X_1,\ldots,X_n$ be a sample in a space with PDF $f_X(x; \theta) = \frac{3}{\theta^3}x^2 I(0\le x \le \theta)$ then caclulate the MLE for $\theta$ and prove that it is an asymptotically unbiased estimator. So far, I managed to calculate $$…
user401305
2
votes
1 answer

Kolmogorov–Smirnov test

We measured time of reaction of 8 drivers right before and 15 minutes after drinking certain amount of alcohol. Times of reaction before were: 0.22, 0.18, 0.16, 0.19, 0.20, 0.23, 0.17, 0.25 and after: 0.28, 0.25, 0.20, 0.30, 0.19, 0.26, 0.28,…
XiaoKa
  • 121
2
votes
2 answers

A tourist in France wants to visit 12 different cities, find the probability.

The Question : A tourist in France wants to visit 12 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order? I thought about this in two ways and I got two different…
shnisaka
  • 213
2
votes
2 answers

Random placement of rooks on a chessboard

$8$ rooks are placed randomly on an $8\times 8$ chess board. What is the probability of having exactly one rook each row and each column? I guess there is no meaningful order here?
Ilona Shishov
  • 37
2
votes
1 answer

How many degrees of freedom?

I have another question on my stats homework, relating to degrees of freedom. However, I have NO idea how this question even relates to degrees of freedom! I understand degrees of freedom on their own, i.e. how when calculating standard deviation…
Laura R
  • 35
1 2 3
…
99 100