Mathematics Stack Exchange
Mathematics Stack Exchange

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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Find the posterior distribution

Suppose that $X_1,\ldots,X_n$ is a random sample from $U(θ,θ+1),$ and further assume $θ$ has a prior distribution as the discrete uniform distribution on the integers $1,2,\ldots,n$ where $n$ is known. Obtain the posterior distribution of $θ.$ The…
MGF01
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Normal Approximation: Getting $E(X)$.

When we use normal approximation to a binomial distribution $Bin(n, p)$, do we assume it is a normal distribution and get $E(X)$ with $E(X)= \int_{-\infty}^{\infty}xf(x)dx$. Or get $E(X)$ as a binomial distribution first with $E(X) = np$? What…
A_for_ Abacus
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How can I tell if dice are biased or unbiased, given a number of trials?

If I'm given the outcome of a number of dice rolls (say, 5 twos, 8 threes, etc), is there a way to assign a probability that the dice are biased or unbiased? If so, how? Or alternatively, how can I say with a given level of confidence that the dice…
BlueRaja - Danny Pflughoeft
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Geometric Distribution: Tossing a Coin Question

Suppose that $A$ tosses a coin which lands heads with probability $p_A$ and $B$ tosses a coin which lands heads with probability $p_B$. They toss their coins simultaneously over and over again, in a competition to see who gets the first head. The…
A_for_ Abacus
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Standard Error of Median

The following question is from Modern Mathematical Statistics (Devore). Consider the following observations: 0.83, 0.88, 0.88, 1.04, 1.09, 1.12, 1.29, 1.31, 1.48, 1.49, 1.59, 1.62, 1.65, 1.71, 1.76, 1.83 Assume that the distribution of the…
Caerus
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Why would $L \ + \frac{f_{m}-f_{m-1}}{(f_{m}-f_{m-1}) + f_{m}-f_{m+1}} \cdot w$ correspond to the mode of grouped frequencies?

$\text{Mode} = L \ + \frac{f_{m}-f_{m-1}}{(f_{m}-f_{m-1}) + f_{m}-f_{m+1}} \cdot w$ where,        • L is the lower class boundary of the modal group.        • fm-1 is the frequency of the group before the modal group.        • fm is the frequency of…
Zac
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Show that a pivotal quantity has a chi-square distribution

Let $Y$ be a random variable with an exponential distribution with E(Y)=$\theta$. Show that the pivotal $\frac{2Y}{\theta}$ has a chi-square distribution using moment-generating function technique. What I did: Mu(t) = E(e$^{tu})$ =…
Ham Sandwich
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Determining If 2D Collection of Points Are Random Or Not

Please forgive the lack of depth in respect of my mathematical vocabulary. I have searched quite a bit in order to determine the answers for myself, however, if you don't know what mathematical/statistical terms to search for, it can be…
CapnAhab
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Computing sample proportion

Was never really taught the use and interpretation of sample proportions explicitly. I tried to work through the first part of this problem above. Did I go wrong at any point?
aero26
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Why does sum of independent uncertainties in General Propagation of Error equal to zero?

In my physics class, we've been doing uncertainty problems with the General Error Propagation Equation. However, I felt uncomfortable using the equation without understanding its derivation. So I was reading this webpage…
Tazik_S
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Odds of two names appearing together in a print ad - help with a gift to boyfriend.

A print ad (for Loving Embrace pendants) used my name, Jennifer and my boyfriend's name, Matthew in their sample pendant. What are the odds that those two names would be choosen? Howmanyofme.com shows that there are 1,521,455 Jennifer's in the US…
Jenicol
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What is the meaning of the word parameter in the context of statistics?

Question: The per capita consumption of bottled water in the United States amounted to 27.6 gallons in 2009. Bottled water is drinking water (carbonated or still) sold in plastic or glass water bottles. Per capita consumption of bottled water in…
yre
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Variance formulae

I know that the variance formula is $$\sigma^2 = \frac{ \left( x_1 - \bar{x} \right) ^2 + \left( x_2 - \bar{x} \right) ^2 + \dots + \left( x_n - \bar{x} \right) ^2 }{n}$$ Where $\sigma^2$ is the variance; $x_1,\ x_2,\ \dots,\ x_n$ are…
JnxF
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Expectation of minimum of $n$ samples from Gaussian distribution

Suppose we have a normal distribution with mean $\mu$ and variance $\sigma^2$. Suppose we draw $n$ samples from this distribution. What is the expectation of the minimum of these samples?
user14717
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Estimation with method of maximum likelihood

Can anybody help me to generate the estimator of equation: $$Y_i = \beta_0 + \beta_1X_{i1} + \beta_2X_{i2}+\cdots+\beta_4X_{i4}+\varepsilon_i$$ using method of maximum likelihood, where $\varepsilon_i$ are independent variables which have normal…
Johnny
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