# 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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### Permutations of a sequence of words

I've been given a question in class and I just wanted to confirm the answer ...
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### Is the result of this inquiry statisticaly significant?

So, my family member asked me for help. I was good at math in high-school but I will only have statistics later in collage. Basicly what he asked me for is to - count the p-level - determine if the ...
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### hypothesis testing two sample problem and standard error of mean

In my homework, I was asked to find the standard error of mean for 2 cases and then do the 5% and 1% test for both of them. I know how to work out stand error of mean, but I don't know how to use it ...
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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 ...
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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, ...
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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: ...
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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 ...
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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 ...