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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What's the variance of an odds ratio?

I know that $$\log(\hat{\psi}) \sim N\left(\log(\psi), \frac{1}{n_{11}} + \frac{1}{n_{12}} + \frac{1}{n_{21}} + \frac{1}{n_{22}}\right),$$ so what's the distribution of $\hat{\psi}$? Note that $\displaystyle\hat{\psi} =…
Adrian
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Differences between two formulations of the Lehmann-Scheffe Theorem

I have seen different formulations of the Lehmann Scheffe Theorem but am not sure if they are the same. For example, on wikipedia it states: If $T$ is a complete sufficient statistic for $\theta$ and $E(g(T)) = \tau(\theta)$, then $g(T)$ is the…
user321627
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Rock drawing possibility

In the latest episode of Survivor there were 6 people and they had to draw rocks from a bag. In the bag were 6 rocks, 5 white rocks and 1 black rock. First person drew a rock and kept it in his hand. Then the second person drew a rock. Last person…
Fsantus
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Existence of complete sufficient statistic

I'm trying to solve a problem in problem list of qualifying exam. Here is my problem : Let $X_1, \ldots, X_n$ be a random sample from a p.d.f $f(x,\theta) = \theta f_1(x) 1_{(-\infty,0)} + (1-\theta) f_2(x) 1_{(0,\infty)}$ where $f_1 \geq 0 , f_2…
user88914
  • 529
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Rough trend calculation and approximation error

In many cases calculating trend by using least-squares method is best decision. But sometimes it is overabundant. What I need is just to know, whether trend is positive or not. Can I use such approach (difference in weight coefficient) and how to…
Pavel Tkackenko
  • 123
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2 answers

Proportion of Values

I'm not quite sure how to do this problem: Calculate the the proportion of values that is 3 in the following data set: 2, 3, 3, 6, 9
Sarah
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1 answer

Filling out a Joint Distribution Tables Given the marginal distributions.

Hello I am trying to figure out how to fill out a joint distribution table when I am only given the marginal distributions. $$ \begin{array}{c|ccc|l} _{\large X}\backslash^{\large Y} & 0 & 1 & 2 \\ \hline 0 & \text{?} & \text{?} & \text{?} & 0.5…
faschijp
  • 33
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1 answer

Expected area of rectangle

This question is taken from Rice - Mathematical statistics. A random rectangle is formed in the following way: The base, X, is chosen to be a uniform [0, 1] random variable and after having generated the base, the height is chosen to be uniform on…
Little Rookie
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Chauvenet's Criterion - All my data points are outliers?

I have runtimes for requests on a webserver. Sometimes events occur that cause the runtimes to skyrocket (we've all seen the occasionaly slow web page before). Sometimes, they plummet, due to terminated connections and other events. I am trying to…
dave mankoff
  • 123
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Ordinal vs nominal variables

Im studying data analysis and Im with a doubt between nominal and ordinal variables, because sometimes it seems difficult to understand really what kind a variable is. For example, about nominal variables there is no meaningful rank between the…
Jody
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expected value and variance of function

I am confused about calculating the expected value of a function that is split, the question looks as follows: and my solution is: Which are incorrect.. can someone please help me to correct the answers. Or tell me what I'm doing wrong. Thank you
amine
  • 161
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Intersection between $2$ sample sets of large lists

Say I have a List A of $1,000,000$ values, and List $B$ of $2,000,000$ values. I want to know what percent of List $B$ is in list A without looking at all $2,000,000$ values and referencing List $A$. So, I want to only look at some of list $A$ and…
Dan
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Understand simple problem on inflation

If the average food basket costs $100$ euros at 2nd quarter prices, how much will it cost for 3rd quarter prices? Below is the graph. I know that the answer is $97$ and can be achieved using follows: $$100 \left( 1 -…
Programmer
  • 233
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Probability that parents don't name their children with the same first initial as their own

To test the hypothesis that parents name their children without bias towards their own initials we have data of one parent name and one of their children's names. There are 600 data points and it has been measured that roughly 7% of parents have…
CallumDA
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Calculating combined percentiles?

How to calculate combined percentile in the following case? Suppose some GMAT-like test result is expressed in two number, V (0-100) and Q (0-100). And to calculate the total score, a simple arithmetic mean is used (V+Q)/2. Now Alice has a score of…
Gerry Lufwansa
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