# 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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### What is a “moment” in mathematics, and what does it mean?

This is a general question. I would like a better conceptual understanding of what a moment is, it's meaning, and it's applications (not just in probability). I already looked at Wikipedia, but I ...
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### How do I find the $Z$ value and calculate the $P$?

Please DO NOT answer the question, as I just need the right formulas in the form of plugging the numbers from the word problem into it. I struggle with this. And I need to find what the percentage is ...
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### Problem calculating the probability that the mean score is less than a certain value.

I'm quite new to statistics and I'm having some trouble solving this problem: An unbiased dice is thrown $70$ times. Find the probability that the mean score is less than $3.3$. Here's what I ...
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### Probability density function: what's a measure $X_*P$?

The Wikipedia article on PDFs defines the probability distribution of a random variable $X$ in $(\mathcal{X},\mathcal{A})$ to be the measure $X_*P$ on $(\mathcal{X},\mathcal{A})$. I understand what a ...
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### Wald Test Statistic

I am trying to understand the Wald test statistic as explained at https://en.wikipedia.org/wiki/Wald_test . What I do not understand is the parameter R in the test statistic: H0: R*theta = r I ...
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### Using the Law of Total Probability to Show

I'm really struggling with understanding how to use the Law of Total Probability in proof questions such as this one. Any help would be hugely appreciated. The number of emails received in a day has ...
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### Finding $P(X+Y=10)$ when $X$ and $Y$ are both of geometric distribution

I am having difficulty finding $P(X+Y=10)$, given that $X$ and $Y$ are independent and both are geometrically distributed: $$P(X=k)=P(Y=k)=p^k(1-p), \ \ \ k=0,1,2,...$$ I attempted to set $X=10-Y$ ...
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### Total accumulated risk

I'm a big fan of Minesweeper. Like other fans, I know that probabilities are important in this game. So, for more fun, I play on this player : http://mrgris.com/projects/minesweepr/demo/player/. ...
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### Prove that the Expected value of Y bar ^2 = µ^2

I'm trying to show whether or not $\bar(Y^2)$ = $\\µ^2$ Or the mean of the sample squared) is a biased or unbiased estimator of the population mean squared. I can prove that Ybar is an unbiased ...
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### Upper bound on an expectation

I'm looking for an upper bound on $E(X^k)$ where $X$ is a random variable with $E(X)=1$. How can I go about doing this?
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### Drawing balls from a box based on die toss

Two boxes, the first contains 3 red & 2 white balls. The second box contains 4 red & 7 white balls. A fair die is tossed. If the outcome is even, a ball is drawn from the first box, while a ...
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### Help: Setting a Discrete Joint table.

My first question is: If i did correctly the next table. For later calculate the asking probabilities.Thanks, again. I follow the advise of kitman0804, and I worked in build the correct table, here ...
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### Need way to statistic puzzle

Hello guys i need help with statistic problem. The problem is : In room have 3 doors, one door is exit from room (o minutes) , second is return us to the room after 3 minutes , and last door is ...
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### How to calculate the expected value on this example, part b, only.

A girl scout troup has 100 boxes of cookies to sell. Of these 100 boxes 60 are chocolate chip and 40 are sugar cookies. 10 boxes are randomly selected to be sold at a fair. (a) What is the ...
Let $T_i$ for $i=1,2,...$ be a sequence of i.i.d exponential random variables with common parameter $\lambda$. Let $N$ be a geometric random variable with parameter $(1/(p+1))$ that is independent ...