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Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, 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 mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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Show that the LS estimator b is unbiased for $\beta$ when regressing without intercept

Okay so I have gotten down to $$b=\beta + \frac{\sum_{i=1}^{n}x_i \varepsilon_i}{\sum_{i=1}^{n} x_i^2}$$ but I cannot figure out how to show that second term is $0$.
Gamecocks99
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Colored blocks and towers

George got a big box from his parents. In this box are colored blocks. He has white, black, red, blue and orange blocks. These blocks are all exactly the same size and of he has the same amount of blocks for each color. George will build towers of…
user106280
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How is a Brownian motion a collection of random variables

In financial mathematics textbooks I have seen it described as a collection of random variables (in the statistics sense of the term random variable), but is that just because at any given moment, there is a subsequent distribution of prices? So…
Arthur Collé
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Prove $E(|X-\mu|) = \sqrt{\frac{2}{\pi}}\sigma$

Prove $$E(|X-\mu|) = \sqrt{\frac{2}{\pi}}\sigma,$$ if $X$ is a normal random variable with mean $\mu$ and variance $\sigma^2$. I don't know where to begin with this problem and would like help! Thanks
user73229
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$Z_1$, $Z_2$, and $Z_3$ are independent standard normal variables. Obtain the correlation matrix

Define $X_1= 2Z_1 - Z_2 +3Z_3$ $X_2=Z_1 + Z_2 - Z_3$ $X_3 = 3Z_1 + 2Z_2 + Z_3$ So would the correlation matrix of $(X_1, X_2, X_3)$ just be the coefficients of each variable?
Gamecocks99
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Minimum number of data points for RMS

In calculating the rms of a group of data points, what is the smallest number of points needed to get a meaningful rms value? Specifically I'm looking at audio files and using an rms value for a small period as a measure of the sound energy for that…
FlyingWeagle
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Grade 9th middle school question

the mean of 5 apple is $12$, the range of the biggest and the lowest is $6$. If every apple is subtracted by $a$ then the sum is divided by $b$, the new mean is $2$ and the range of the biggest and the lowest is $3$. Find $a$ and $b$.
Jeniffer
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The joint pdf of the amount X of almonds and amount Y of cashews in a 1-lb can of nuts

The joint pdf of the amount $X$ of almonds and amount $Y$ of cashews in a 1-lb can of nuts was: $f(x, y) = \begin{cases} 24xy & 0 \leq x \leq 1,\, 0 \leq y \leq 1,\, x + y \leq 1\\ 0 & \text{otherwise}\end{cases}$ Obtain the marginal pdf of the…
Fred
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Relation of parameters of fitting lines

Scientists want to find the relation between two variables $x$ and $y$ by line $$y=ax+b.$$ After some experiments, scientist $S_i$ find the best parameters are $(a_i, b_i)$. It is sure that different scientists find different parameters. The…
Ma Ming
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meaning of math symbol in probability expression?

anyone knows the meaning of the marked symbol in the pic and its Latex syntax?
user20835
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Contingency table on Bayers Rule

The question is this: A medical test for the disease StatsLove will correctly state that a diseased student suffers from StatsLove 95% of the time. The medical test correctly states that a non-diseased student does not suffer from StatsLove 99% of…
hlx98007
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How do you calculate an upper-confidence bound on a problem with 2 means?

I am presented with: Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be σ1 = 0.10 and σ2 = 0.15 fluid ounces for the two machines, respectively. Two random samples of…
rphello101
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What on earth is (B|A)?

I'm stumped and getting nowhere with this question: Description: The Air Pollution and Mortality data of 60 cities were collected in a study. 11 can be considered to have high hydrocarbon pollution potential levels. Suppose that two cities are…
JimmyB
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Random Probability Question

Suppose you throw m=12 balls into n=8 bins. Let Xi be the number of balls that fall into bin i. Let Ti,j Be a random variable that is 1 if the j’th ball falls in the i’th bin. Clearly Ti,j,Ti,k are independent for 1≤j What is Pr(Xi=0)? What is…
Raj
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regression without intercept

i just want to clarify if the estimator for a ordinary least square regression without a intercept consistent. I could prove that it is biased but im not how to prove whether it is or not consistent. Someone pls advise.
Davin
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