# 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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### Marginal Density Question

I am faced with the following question, which I think is quite simple, but I can't put together for some reason. Given that $f(x,y)=(6/5)(x+y^2)$ for $0<x,y<1$, ($f(x,y)=0$ everywhere else), I ...
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### Fast way to recalculate average and standard deviation as new values arrive

Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...
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### exactly, and at least : Probability

thanks for looking at my question. Any help would be appreciated! at a university 60% of the students are male and 40% are female If ten students are selected at random, what is the probability that ...
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### Combinations/probability calculations using ball/bag analogy

I'm wondering how to approach this question? I'm analysing data for a research project, but I feel like it falls into the category of choosing combinations of balls in a bag. Any help would be much ...
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### Why MLR (monotone likelihood ratio) implies stochastic increasing?

the following argument holds: for $\theta_1<\theta_2$, $\dfrac{f(x\mid\theta_2)}{f(x\mid\theta_1)}$ is increasing in $x$. Then, $F(x\mid\theta_2)\leq F(x\mid\theta_1)$ for all $x$. Intuitively, ...
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### Is a 99% upper confidence bound the upper limit of a 99% confidence interval?

I have to find a "99% confidence bound" for a standard deviation. This is not hard. The only question I have is whether this is finding the $\chi^2_{.99}$ value or just the upper bound for the 99% ...
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### Probability Dice Game Question

I have the following problem to solve that deals with probability (something I haven't done since Grade 8 (6 years ago)) This is a one player game and it is described for $q$ sided dice. You start by ...
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### Inequalities that show if a distribution decays slowly

Often, one is often interested in theorems/inequalities of the following kind: Let $X$ be a random variable then the probability that $X$ is close to typically $\mu$ (or larger than some constant) is ...
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### What does multiplication mean in probability theory?

For independent events, the probability of both occurring is the product of the probabilities of the individual events: $Pr(A\; \text{and}\;B) = Pr(A \cap B)= Pr(A)\times Pr(B)$. Example: if you ...
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### Hypergeometric Distribution Question

In a hypergeometric distribution, you can compute the probability of drawing without replacement, which is useful in a number of studies and statistics. However, I'm having a problem that I've had for ...
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### Probability of choosing a subset of elements where each element has a different probability

I am trying to write a C++ program to do this but nobody on Stackoverflow can seem to help me so I thought I'd try to do it myself with some help from you guys. My post on Stackoverflow can be found ...
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### Probability of 2 identical events

My professor said that probability of 2 identical events in a very short amount of time (dt converges to 0) is 0. However, I did not agree with him about this. Is there a proof for that assertion? ...
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### Expanding variance

Could someone please expand on line 2 and 3 of: Thank you.
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### Two Expected value definitions of the geometric random variable

Ok so I'm looking at my book and it defines the geometric distribution to be $\sum_{i=1}^{\infty}p(1-p)^{n-1}$. My book says the expected value of a geometric random variable is $\dfrac{p}{q}$. It ...
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### Probability density function help

If a random variable is given by $Y=aX+b$ where $X$ is a random variable does that mean $aX+b$ is $Y$'s pdf?? and if i wanted to find $E[Y^2]$ would this just be the same as finding $E[(aX+b)^2]$ and ...
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### Calculating probability of a dice with different numbers

I was given a problem in class: ...
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### Expected value given that distribution is positive vs. conditional expectation

Referring to Expected value of normal distribution given that distribution is positive Where is the difference between $E(X$1$_A)$, where $A=[X>0]$, and $E(X∣A)$? Both seem to express the ...
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### Expectation value with condition

how can i show that: $E[XY \vert X ] = XE[Y \vert X]$ for two random variables $X$ and $Y$ sorry this must be wrong what i meant was $E[ E[XY \vert X ] ]= E [XE[Y \vert X]]$
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### Joint PDF of all n Order Statistics

If $X_1,\ldots,X_n$ is a random sample from a continuous distribution with pdf $f_{\theta}(x)$, why is the joint PDF of the order statistics $X_{(1)},\ldots,X_{(n)}$ the following: \large f_{X_{(1)},...
You are given an array $A[0 \ldots n-1]$ of $n$ numbers. Let $d$ be the number of \emph{distinct} numbers that occur in this array. For each $i$ with $0 \leq i \leq n-1$, let $N_i$ be the number of ...