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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.

37109 questions
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what is the critical region of the following hypothesis test?

Let $X_i$ ($i=1,\dots, n$) be a random sample from $X\sim \exp(\lambda_1)$ and $Y_j$ ($j=1,\dots, m$) be a random sample from $Y\sim \exp(\lambda_2)$, and $X$ and $Y$ be independent. I try to find the generalized test of $H_0: \lambda_1=\lambda_2$…
Hermi
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Statistics: Reconciling with different variance and expectation formulas

I am trying to understand these two definitions, but I'm just not clear where they come from and how they relate to the old formulas that I was used to a week ago. In one book variance is defined as: $\displaystyle Var(X) = \int (x-\mu)^2 f(x) dx $…
Person
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How confident am I to say the coin has been rigged

Let's just say that I flipped a coin 100 times, got 80 heads and 20 tails, how confident am I to say that the coin has been rigged? Which statistical test should I use? thanks!
arax
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Expected Value of maximum nesting in iterative group procedure

Whilst working on random test data generation I came across the following problem, I have a List of Lists, L, where each list contains objects an object is either a "thing" or a group of things ( $t$ or $\{t,...\}_g$ ). Initially there are no groups…
Sam Coutteau
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Interaction effect in ANOVA .

The statistical model for a Randomized Complete Block Design (RCBD) with multiple observations per cell is $$y_{ijk}=\mu+\tau_{i}+\beta_{j}+(\tau\beta)_{ij}+\epsilon_{ijk},\quad i=1,\ldots ,a, \quad j=1,\ldots, b,\quad k=1,\ldots, s, $$ where…
ABC
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confidence intervals - a bad confidence interval

I had a question for confidence intervals: the situation in the question :so we have a number of scatter plots with each showing an estimated regression line (based on a valid model) and associated individual 95% confidence intervals (CI) for the…
Raditz
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Normal distribution finding P area

Q: let X be a continuous random variable with NORMAL DENSITY $$f(μ,σ(x)) = \frac{1}{\sqrt{2}π}*σ *e^{−(x−μ)^2/ 2σ^2}$$ We know that $μ = 70$ and $σ = 2$. Find $P(68 \leq X \leq 74)$ and $P(X \geq 73)$: my approach is ... Since above is normal…
Levy
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Trying to understand an equation for predicting baseball, specifically a comma?

I'm reading a paper about predicting baseball games, and I'm having trouble figuring out what one of the variables means. It's the "r1, r2, and r3" variables in the following passage: It is unreasonable to expect that all three ratios affect…
jstewartmitchel
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Fischer's Discriminant for Multiple Classes, why are there $c-1$ discriminant functions

I'm reading about Fischer's Discriminant for multiple classes. In Duda and Hart's Pattern Recognition they write that For the $c$-class problem, the natural generalization of Fisher’s linear discriminant involves $c − 1$ discriminant…
IntegrateThis
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Suppose that $X\sim\operatorname{Binomial}\left(n,p\right)$ and $Y = n - X$. How do I find $\mathbb{E}\left[XY\right]$?

Consider a sequence of $ n $ independent bernoulli trials with a success probability of $ p $. Let $ X $ be the number of successes and $ Y $ the number of failures. Find $ \mathbb{E}\left[XY\right] $. So, I'm kinda stuck in this exercise. I tried…
Stats...
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Inverse/Rejection Sampling

How can I simulate using Inverse and Rejection method for $f(x)=\left\{\begin{matrix} \frac{1}{2} & 0\leq x\leq 1 \\ \frac{1}{4} & 2\leq x\leq 4 \\ 0 & otherwise \end{matrix}\right.$ I found the cdf $F(x)=\left\{\begin{matrix} 0 & x <…
user1016882
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Justification for normalization in a ratio scale data

Without loss of generality, I asked a group of participants $X=\{x_1,x_2,\ldots ,x_m\}$ to give scores in a $L$-point ratio scale $0,\ldots,l$ to different items $C=\{c_1,c_2,\ldots ,c_n\}$ based on the relative importance. They are asked to give at…
River
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Point estimation - Definition confusion

I am reading about MLE (Maximum likelihood Estimation). And I had to also read about the Point estimation, for which the following was said: "In statistics, point estimation involves the use of sample data to calculate a single value (known as a…
imbAF
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Ask the expectation of sample variance in terms of $X_i$ and $X_j$

Let $X_1,..., X_n$ be a random sample. Then one version of the sample variance formula is $$S^2 = \frac{1}{2n(n-1)} \Sigma_{i=1}^n \Sigma_{j=1}^n (X_i - X_j)^2$$ Then suppose $n = 4$ and $E(X_i)=0$, I know $S^2 = \frac{1}{24} \Sigma_{i=1}^n…
Jonathen
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Unbiased estimator of $\theta$, where is a random sample of $X_1,...,X_n\sim$ Uni$[\theta,0]$ for $\theta<0$.

My attempt: We observe that since $X_i\sim$ Uni$[\theta,0]$, then $X_i=-\theta U_i$ where $U_i\sim$ Uni$[-1,0]$, with $U_i$ independent. We estimate $\theta$ considering the minimum of the random sample. Since $U_i$ are i.i.d, we observe that for…
GaloisTH
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