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

Mode of a frequency distribution with unequal class length

How can I find the mode for a grouped frequency distribution with unequal class lengths? I have to find the mode for the following problem: \begin{array}{c|c} \text{Marks} & \text{# of Students} \\ \hline \text{0 - 20} & 32 \\ \hline \text{20 - 50}…
user3575652
  • 347
2
votes
1 answer

Can someone give me an idea of finding the distribution of $\frac{\sum_{i=1}^N (X_i-E(X))^2}{\sum_{i=1}^M (Y_i-E(Y))^2}$

X~N(4, $\sigma^2$) and Y~N(1, $\sigma^2$) are independent. $$A=\frac{\sum_{i=1}^N (X_i-E(X))^2}{\sum_{i=1}^M (Y_i-E(Y))^2}$$ Find the distribution of A? I tried this way. $$\frac{M-1}{N-1}A=\frac{\frac{1}{N-1}\sum_{i=1}^N…
Chloe
  • 21
2
votes
4 answers

Likelihood function and MLE

Please let me know how to find the likelihood function and MLE for the function $$f(x;θ) = (θ+1)(x^θ)$$ I have tried using the general formula for likelihood function $L(θ)$ however not sure how to proceed further. Please assist.
Teby Thomas
  • 21
2
votes
2 answers

Around De Moivre–Laplace theorem/Poisson law

The task is: Typist printed 1000 pages of text, and made 140 errors. What is the probability that a randomly chosen page contains zero errors? one? two? The error distribution is described with Poisson law. Using Poisson's law, I got that…
Mikhail Tikhonov
  • 532
2
votes
2 answers

Statistics in circuits

I have a circuit, in order for it to work the electricity has to travel from point $A$ to point $B$, but on its way there it encounters $4$ independent switches. If any one of them is closed the system will function properly. the probability of a…
noahdukeh
  • 23
  • 3
2
votes
2 answers

Ways of characterizing sufficient statistics

I've been reading a little about the Fisher-Neyman factorization theorem on my own, and I think I understand intuitively what a sufficient statistic is, but I am wondering what the convention is for formally defining it. Is it true that, for a given…
Greg Nisbet
  • 11,657
2
votes
0 answers

Calculate SE from a Given Margin of Error

I have data from the Census bureau that has means and margins of error that are defined at 90% confidence. For example, a zip-code population estimate of 17042 with a 90% moe of 278. I'd like to do some inference based off of this data, but I need…
gelly_belly
  • 21
2
votes
2 answers

Using the Central Limit Theorem to work out the approximate distribution of $\frac{1}{n}\sum_{i=1}^nX_i^2$

Suppose $X_1,X_2,\ldots,X_n$ are I.I.D $N(0,1)$. Then, what is the approximate distribution of $\frac{1}{n}\sum_{i=1}^n X_i^2\,$? I have the solution but none of it is making any sense to me. Thank you for your help!
THISISIT453
  • 664
2
votes
1 answer

Unbiased estimator of $\int_0^t \mu (s) ds$

Let $\mu,\alpha_n:\mathbb R^+\to \mathbb R$ continuous function with $\mu$ bounded function. Let $N^{(n)}$ the trajectory of a Poisson process with intensity $(\alpha_n \mu)(t)$. Let $0=T_0^{(n)}
user298629
  • 21
2
votes
2 answers

Let $X,Y \sim N(0, 1)$. Find $E[X\mid X+Y=1]$.

Assume the joint distribution for X, Y is also normal. I have no clue how to approach this problem. Follow up question: Without knowing the joint distribution of X, Y can you still calculate it?
butterbetter
  • 351
2
votes
0 answers

Bias of two estimators

I hope someone can help me. I have some trouble calculating the bias of two estimators.Unluckily it is really urgent because I hold a presentation next week. The topic is nonparametric local regression. In order to compare kernel estimators I have…
user143352
  • 21
2
votes
1 answer

Mean of interpolated data or interpolation of means in geostatistics

Say I have a time series, with actual measurements of a variable $a$ in different locations. If I want to know the average of $p$ from time $t_1$ to $t_n$, I could say that $\overline{a_{p}}=\frac{\sum\limits_{t=1}^n a_{{p}_t}}{n}$, where $p$ is…
Adriano
  • 21
2
votes
1 answer

How to calculate if taking a toll road is worth it

I'm trying to figure out if there's a way to calculate if it's worth taking a toll road if it will save me time. For example, if the toll only costs 50 cents and my trip will save me 30 minutes, I will take the toll. On the other hand, if the toll…
splungebob
  • 123
2
votes
2 answers

Please Explain a simple Formula, calculating time in-between a call queue

I have a simple algebra formula, proven to work. But I need help in understanding why it works. The Scenario: I work at a call center, and am trying to calculate the time free in-between calls. I have the 3 variables, provided by Live data: Staff…
user2861921
  • 23
2
votes
1 answer

Statistical method to prove that variations are not important?

I'm checking the effect a specific substance has in the elongation of the root of variousplants of the Solanum genus. I had my plants grow in soil with different concentration of hormones. My results are quite obscure from what I expected, so I'm…
user259462
  • 31
1 2 3
…
99 100