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
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Finding $E(\bar{X^2}|\bar{X})$

Possible Duplicate: Finding $E\Bigl(\overline{Y^2}\Bigm|\overline{Y\vphantom{Y^2}}\Bigr)$ by Basu's theorem? Suppose $X_1,\ldots,X_n$ are a random sample of $N(\theta,1)$. if $\bar{X^2}=\displaystyle\frac{1}{n}\sum_{i=1}^n X_i^2$, how can I find…
hadisanji
  • 999
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How many boys and girls should be included in the sample.

This is a statistics related question which follows an introduction to stratified sampling. A survey to estimate the number of vegetarians in a mixed college with 660 boys and 540 girls is carried out. A sample of 40 students is required. How many…
Kantura
  • 2,721
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Statistics - Expectation of OLS residual squared

Suppose that $y = \beta_0+\beta_1x + \epsilon$ where $\operatorname{E}[\epsilon\mid X]=0$ and $\operatorname{Var}[\epsilon\mid X] = \sigma^2$. In what special case is $\hat{\epsilon_i}^2$ an unbiased estimator for $\sigma^2$? Is $\hat{\epsilon_i}^2$…
Eric Xu
  • 179
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Needing to find a variance from a data set below

I am trying to get the variance of the data set below. I get a negative number upon applying 1/2(2.5)^2 + 1(3)^2 + 0.5(4.5)^2 + 1(5)^2 + 1(6)^2 - (17.5)^2 = variance, but a negative and weird number. Please use this data below from the link, the…
mary
  • 2,374
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Limits on median given mean and sd

Given N, a mean, a standard deviation, and the range, what does that tell us about the median? Obviously and trivially it must be within the range, but can we get tighter limits? To give context, I'm trying to find a median by repeated search. I may…
Malcolm McLean
  • 121
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chi squared additive property + subtraction property question

so I got questions a + b right but when I got to c I made a couple of mistakes. Can someone tell me how to do c? I thought I was doing it right but I got the degree of freedom wrong and the symbols. old answer:
NookLines
  • 361
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Consistent estimate using likelihood function

Let be $X$ a population with normal distribution. Using likelihood function I get the below expression $\hat{\sigma_X}^2 = \sum_{i=1}^{n}{\dfrac{(X_i-\mu)^2}{n}}$ for variance. I want prove that expression is consistent, i.e.…
juaninf
  • 1,264
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Paired t-test: More distance results in lower p-value?

In my test I alter one parameter in three stages (p1 After plotting it, it is quite obvious that the parameter positively effects the outcome, because all 3 lines are above each other (no intersection). However, when I do the 3 paired t-test (p1 vs…
UKWildcats
  • 21
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Probability to see all 6 numbers on a die after n throws

I am trying to work out the probability of seeing all 6 numbers on a fair die at least once after n throws, where n > 6. So I found a related question: Probability of rolling a dice 8 times before all numbers are shown. and a part of the provided…
Peter
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Statistics: Testing hypothesis

I'm not sure that I'm understanding this stuff fully so I would appreciate it if someone could check my work. QUESTION The percentage of children who leave foster care due to adoption is generally accepted to be 15%. A social worker claims that…
user354704
  • 21
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Expected Number of flips for alternating Heads/Tails 10 times

What is the expected number of flips needed to flip a coin 10 times and have the outcome be alternating heads/tails (starting with heads, then tails, then heads etc...). I wrote a c++ program and it gives me 2,730. Is this correct and how would you…
arslan sana
  • 31
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What test would I use to analyze an applications' error rate?

I am a software engineer with a stats problem: I want to deploy a new version of a web application to a subset of users, measure the error rates, and if there is not an increase of error rates, direct it to all users. (We call this 'Canary…
Dan Alvizu
  • 121
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Odds of 1 out of 7 NFL teams making the playoffs

I have a potential prop bet in the making where my opponent has to pick 7 NFL teams not to make the playoffs for this upcoming season. If all 7 of their teams miss the playoffs, they win, if at least 1 of their teams make the playoffs, I win. I've…
Harley
  • 21
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VC Dimension of star-shaped sets on $\mathbb{R}^2$

Consider a set $U \subset \mathbb{R}^2$ to be star-shaped with respect to a point $\epsilon \in \mathbb{R}^2$ if for every $x \in U$, the segment joining $\epsilon$ and $x$ is contained in $U$. Consider the $H = \{U \subset \mathbb{R}^2 | U \text{…
Brittney
  • 169
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Show that $n \to \infty, \sqrt{n}(Y_{n}-p) \rightarrow N(0,p(1-p)$

Can anyone show me the correct working out to find the variance for $Y_n$, My variance seems to be $\frac{p(1-p)}{n}$
HueHue
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