Mathematics Stack Exchange
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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.

37109 questions
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Comparing the variances of two distributions

$X$ and $Y$ are discrete random variables with means $x$ and $y$ and variances $V_x$ and $V_y$, respectively. Does the ratio $V_x / V_y$ have meaning, and, if so, what is it?
user1505713
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sale price, interest per annum and percentage increase or decrease

Mary bought a computer on hire purchase. If the cash price on the computer was $3 million and 25% was down payment if bought on hire purchase. If the balance was paid in 12 monthly installment at 12% interest per annum. Find the percentage increase…
norah kappy
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Beta distribution, find the general expression for $E(X^{r}(1-X)^{s})$.

I have the following question given to me about the beta distribution. I have been stuck on this one for hours now. Let $X$ have a beta distribution with parameters $\alpha$ and $\beta$, let $r$ and $s$ be given positive numbers. Find the general…
Stewart
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Why is chi-square statistic not dimensionless?

I figure, if I measure something in meters, and then take a chi-square from it to test a hypothesis, the value I get will be in meters too. But that doesn't make sense: by simply switching to kilometers, I'd get a 1000 times smaller value. Or is it…
Dima
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Weighted product vs. weighted sum

I've been searching for almost a day now and I'm running out of steam... can someone give me a nice, easy to grasp explanation/example of what a weighted product does compared to what a weighted sum does? I'm having trouble coming up with an…
Managarm
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Uniform Integrability - proof

I came across a proof for the following proposition. However, there is one part of the proof which I don't understand. The proposition and proof are as follow. Proposition: A nonempty family $\mathcal{X} ⊆ L^0$ is uniformly integrable if and only if…
user372128
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Use moment generating function to show that $f_Y(y)$ has chi squared distrubution

Problem in my Stat class Let $Y_1, Y_2,\ldots, Y_n$ be arandom sample of size $n$ from $$f_Y(y)= \frac{1}{\theta } e^{-y/\theta}, \qquad y> 0,\theta > 0$$ Use moment-generating functions to show that the ratio $2n\bar{y}/\theta$ has a chi square…
Postskjerm
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How mean change standard deviation?

A college statistics class conducted a survey of how students spend their money. They asked 25 students to estimate how much money they typically spend each week on fast food. They determined that the mean amount spent on fast food is $31.52$ with a…
Nadia Anderson
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Hmm. help with a tiny statistics question please

This isn't homework, I am boggling my head over it though. I got all sorts of answers, just not the answer my book demands. For what value of $x$ the mean of the given observations $2x - 5, x + 3, 7 - x, 5-x$ and $x + 9$ with frequencies $2,3,4,6$…
Aayush Agrawal
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Statistical Analysis and Techniques

The lifetime in hours of a tubelight is a random variable $X$ having a probability density function $f(x) = 4xe^{-2x}$, where $x>0$. If $Y= -3X+10$, then find the Expected Value of $Y$, and variance of $Y$.
Maitreyi
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How does the parameters of F-Test affects its power?

Suppose we have $z = \frac{u/p}{v/q} \sim F(p, q, \lambda)$ whereby u is distributed as a non-central chi-square with parameters p and $\lambda$. The power of an F-Test is the probability of rejecting $H_0$ for a given value of $\lambda$. If…
user10024395
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a loaded die? Practice

Three dice were rolled. The first two were rolled 25 times, and the third was rolled 50 times. For each die find a number that ranks it relative to the others in terms of how fair it is (or how much its distribution of scores differs from chance).…
user367578
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Model Selection property between AIC and Mallow's $C_p$

Let us consider a set of linear models defined by the function $Y_i = \beta X_i + \epsilon_i, \epsilon_i \sim N(0,\sigma^2).$ Take a model $S$, and define the training error of a given model as $\hat{R}_\text{tr}(S) = \sum_{i=1}^n (\hat{Y}_i(S) -…
Alexander
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basic t-test statistics

I'm writing an article, and I'm on a deadline so please be kind to me, I'd like to test for statistical significance of the difference before and after an intervention but I'm no real math genious My sample size is 63 pre and post-intervention…
Jakob
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How high can a Kurtosis value be?

I am working on computing some summary statistics for a bank that nearly failed during the 2008 crisis. The time series I have is the stock price and returns for this particular bank, spanning 9 years. However, for a period of 5 months in my time…
Ali
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