# Tagged Questions

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 analysis.

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### Finding the distribution of a minimum of a set of variables

I have been working on a problem where $X_1,...,X_n \sim \mathrm{Exp}(\beta)$ are i.i.d. and $Y = \min\left\{X_1^{0},X_2^{X_1},X_3^{X_1+X_2},...,X_n^{\sum_{i=1}^{n-1} X_i}\right\}$ . I want to find ...
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### How to make a covariance matrix from multiple observations of different objects?

I have $N$ objects. From each object, I sample $M$ values $(x,y)$ like so: ...
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### Using coefficient of variation vs standard deviation to understand trial-to-trial variability

The basic model I have is as follows: I'm studying the response time of a neuron that's affected by two sources of noise: intrinsic noise and synaptic noise (i.e. random fluctuations in the voltage ...
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### What is the expected number of throws to get all six faces of dice n times [duplicate]

I want to calculate what is the expected number of throws to get all six faces of a dice n times? (for example expected number of throws to get all six faces 2/3/4 time) ? I already know the negative ...
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### Calculating a three sigma limit on data

So I have a list of data points each with their own error (eg. 3 +/- 0.2 units) and I want to determine which of the data points are within 3 sigma. To do this do I just calculate the standard ...
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### Improving Probability of Event='1' in Logistic Regression (SAS)

I will try to give as much background as I can and if more is needed I will gladly give more. I'm working on trying to find an equation that will tell what probability you have a defaulting on a loan ...
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### Order statistics question

In paper "Gene prioritization through genomic data fusion", they used order statistics to get combined rank for features. enter image description here ri is the rank ratio for data source i, N is ...
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### Weighted Linear Regression

I am performing linear regression analysis on a time-series of data. Data contains some missing values, My question is, if I impute the missing values using mean of all the values and I want to ...
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### How to know when to use t-value or z-value?

I'm doing 2 statistics exercises: The 1st: An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If ...
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### Minimize the sum of distances between a sample and two “centers”

Suppose we have a set of readings $\{X_{i}\}$, each of which is a real number. What I want is to find 2 numbers, $a$ and $b$, such that minimize the sum of distances between each $X_{i}$ and ...
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### Proof that: $I-X(X^TX)^{-1}X^T=((I-X(X^TX)^{-1}X^T)^2$

I have to verify if the statment: $$I-X(X^TX)^{-1}X^T=((I-X(X^TX)^{-1}X^T)^2$$ is true or not. (I do not get to demonstrate). Any help or hint will be very useful for me. Thanks a lot!
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### Bivariate normal distributed vector $X (X,Y)$. Show distribution of $(X-Y, X+Y)$.

I have a a bivariate normally distributed random vector $X = (X,Y)$ and with Expected Value $(X)= (\mu(x),\mu(y))$, and Covariance Matrix $2\times 2$. (not independent) Now I want to show which ...
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### Determining if dice are fair using statistics

A casino must demonstrate to the state gaming commission that every die it uses is fair. a machine is used to roll each die 1200 times. a die is discarded if the following assumption it is fair is ...
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### Rank a pool of $N$ items with validation & weight

I'm not a mathematician and I'm new to this site. Apologies if this question is not formulated correctly. I have a statistical problem I need to resolve. Any help is highly appreciated! I have $N$ ...
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### Create a strictly increasing sequence following criterias

Problem Let y be a sequence of real numbers (of length $n$) bounded in the range [0,1]. I am trying to calculate the sequence x ...
### A question about Chebyshev's inequality and why $\operatorname{Var}(\overline X_n) = \sigma^2/n.$
This is the question: For i.i.d. r.v.s $X_1, . . . ,X_n$ with mean $μ$ and variance $\sigma^2$, give a value of $n$ (as a specific number) that will ensure that there is at least a $99\%$ chance ...