# 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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### Gaussian Approximation of an intractable distribution

I am currently encountering this problem: I have an intractable distribution and I want to minimize the KL divergence of this distribution and a multivariate gaussian distribution. So we just need ...
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### Calculate Linear regression segment [duplicate]

I have array of random numbers. How can I calculate linear regression segment? I am interested in finding the exact formula so I be able to use it in my work, please help me finding this formula with ...
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### Hypothesis testing: how do you call the variable that is being hypothesized about?

The question is easy but it is really hard to find via Google. Say you have the following hypothesis: $H0: \mu = 0$ $Ha: \mu \neq 0$ Now I know that $\mu$ is called the population mean. But how ...
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### Binomial distribution concept?

The equation for binomial distribution is as follows, $$P(x) = \binom{n}{x}\cdot p^x \cdot (1 - p)^{n-x}$$ My question is, why does it multiply the odds of an event firing with the odds of an event ...
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### Finding probabilities with a Poisson distribution

This is the question that I'm stuck with: An airline knows that overall 3% of passengers do not turn up for flights . The airline decides to adopt a policy of selling more tickets than there are ...
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### Propagation of Error question?

If I have a function $$f(r,V,B)=\frac {2V}{r^2B^2} = 2Vr^{-2}B^{-2}$$ what is the propagation of error? If I use the power rules and multiplication rules described here http://www.fas.harvard.edu/~...
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### Can multiple events have more than a 100% chance to fire?

For example, if a pitcher has a 50% chance to hit a ball, and during a game he pitches six times, what are the odds he will hit one ball? I would assume the answer is $0.5 * 6$, or $300$%, meaning he ...
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### Logic behind combinations with repetition?

I've read the stars and bars analogy, but it really doesn't make sense to me. The way I see things, combination with repetition of say 5 of the same color balls in 2 different boxes WITH REPETITION ...
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### If $x_1,\cdots,x_n$ are iid normal with mean 0 and variance $\theta$ unknown, find the Jeffry Prior for $\theta$

So I have the following, $L(x|\theta)=-\frac{1}{2}ln(2\pi)-\frac{1}{2}ln(\sigma^{2})-\frac{1}{2\sigma^{2}}x^2$ Then the first derivative is, $-\frac{1}{2\sigma^{2}}+\frac{x^{2}}{(\sigma^{2})^{2}}$...
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### Accuracy Rate with Timing

I have a test that my students take where I am interested in both their accuracy rate as well as the speed in which it took them to complete the test. The results look like this: Bob: 56/66 400s ...
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### X and Y are two random variables, what is the standard deviation of X - 2Y

I have: E(X) = 10 E(Y) = 12 Var(X) = 4 Var(Y) = 9 covariance = 2 I know that for: Var(X + Y) = Var(X) + Var(Y) + 2covariance ...
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### Logistic regression eye treacting data (need model)

I have two sets of time course data, they are for an eye-tracking study. The data is 20 100ms chunks, one category being percent fixations for canonical sentences, and the other being percent looks ...
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### Let X1, X2, …, Xn be an iid sample of Bernoulli random variables, Find the likelihood function, MLE,sufficiency

a.Find the likelihood function, L(theta) L(theta)=(x1,x2,x3.....xn|theta)= theta^x(1-theta)^(1-x) ? b. find the MLE MLE is theta =x not sure how to show the sufficiency and how to show the MlE as ...
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### Difference of parameters and arguments when dealing with statistics functions?

In 'classic' math when you have a function like $\sin (\theta)$ or $\cos (\pi)$ is pretty straight forward that both should have an argument and it's very simple to see that in this specific case the ...
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### Why does the keyword “distinct” change the solution to much?

I don't understand why the second answer is different from the first. Aren't they the exact same thing? How many ways can we distribute 10 distinct balls into 5 distinct boxes? $5^{10}$ is correct ...
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### Limiting distribution of $X_n1(|X_n|\le 1-\frac{1}{n})+n1(|X_n|>1-\frac{1}{n})$ if $X_n\sim Unif(-1,1)$ and are iid.

Limiting distribution of $X_n1(|X_n|\le 1-\frac{1}{n})+n1(|X_n|>1-\frac{1}{n})$ if $X_n\sim Unif(-1,1)$ and are iid. From looking at the term, if $n$ goes to infinity, then $Y_n$ would be $X_n$ so ...
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### What is the probability that $x_1+x_2+…+x_n \le n$?

Given that $X_1, X_2...$ are mutually independent random variables. For each $i$ with $1\le i \le n$ the variable $X_i$ is equal to either $0$ or $n+1$ $E(X_i)$ = $1$ also.. if $X_i$ is equal to ...
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### How do I find if the probability of the sample proportion is greater than something?

I have this problem and I have no clue how to solve it. In 2012, 31% of the adult population in the US had earned a bachelor’s degree or higher. One hundred people are randomly sampled from the ...
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### Maxima CAS , Statistic Formula with Maxima

I am working on my graduation project which study sport players' performance. I have collected the data and finished all the surveys but then I am stuck at using the following formula to calculate ...
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### Statistics Similar Number in sets

I'am trying to determine what is the likelihood having the same sequence of numbers in a given array. I have an array of 2 rows and n columns (n is known), I then decided a range (1 to x) let's say 6 ...
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### Probability that certain drawn pieces of paper having the same colour are in the same group

I have the following question: I have 12 players and wrote their names on 12 pieces of paper. I put the 12 pieces of paper in a box, but 2 pieces of paper were green-coloured, and the rest was red-...
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### Likelihood Function for the Uniform Density $(\theta, \theta+1)$

Let the random variable X have a uniform density given by $f(x;\theta)$~$R(\theta,\theta+1)$ What is the maximum likelihood function according to the samples $X_1,\ldots,X_n$? The question is much ...
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### probability of getting particular cards in a hand (cards)

I was given the question in class: "What is the probability of getting a hand with 1 heart, 2 diamonds, 2 clubs?" and "What is the probability of getting a hand with at least 3 queens" for the ...