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 a complete sufficient statistics, or show that one does not exist

$$ f(x|\theta) = e^{x-\theta}\exp\left(-e^{x-\theta}\right),\;\;\; -\infty < x < \infty,\;\;\; -\infty < \theta < \infty.$$ Find acompliete sufficient statistics, or show that one does not exists. What I have found was that this given $f$ is not…
Block Jeong
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How to rank a product with 90% score by more number of people better than a product with 100% score by less number of people?

First of all, I really couldn't think of a right way to phrase the question title. Below, I have reduced the problem that I am trying to solve to a similar one that could be easily understood. I searched for similar questions on this forum but…
Ragavan N
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A problem on statistic

If 10 or more defective product are found in quality checking, this batch of products are rejected. At least how many product must be checked to get a probability of 0.9 to reject a batch of products with a defective rate of 10%?
Celvin
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95% Confidence Interval for $\sigma^2$ & Determining the Reliability of the Claim

Question : A manufacturer of car batteries claims that his batteries will last, on average, 3 years with a variance of 1 year. If 5 of this batteries have lifetimes of 1.9, 2.4, 3.0, 3.5 and 4.2 years, construct a 95% confidence interval for…
Casper
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proper statistical test to check differences

I have $3$ replicas for a value in different individuals. Each of these values are ratios $\frac{a}{b}$, and $a$ and $b$ are means from $n=20$ sample pool each. Thus there are $3$ times each ratio $\frac{a}{b}$ for each individual. When comparing…
Katz
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Convergence in distribution to a standard normal

How to show $$ \lim_{n\to\infty}\left(1-\frac{t^2}{2n}-\frac{t^3}{2n^{\frac32}}\right)^{-n}=e^{\Large\frac{t^2}{2}}\,\,? $$ LHS is expanded and approximated form of a moment generating function. RHS is MGF of a standard normal. This is proven in…
xyz
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How to know when to use which test statistic?

I'm studying for my stats exam and I seem to always get stuck on which test statistic to use. This is even after many examples that I have done. For example: With this question: I attempted to do this: $\frac {0.2 - 0.1}{\sqrt{(0.2 \times 0.8)…
Abushawish
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Estimating parameter of random sample

5 random numbers were recorded: 100,32,76,52,17. If we know that these are elements of random sample took from set {1,2, ..., N}, how do we estimate the parameter N?
user142176
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Revenue significance test

I would like to ak if is it possible to make a significance test for revenue from A/B testing when I have these data: | Visits | Transactions | Conversion rate | Revenue | Original Page: | 9127 | 96 | 1,05 % …
Pavel
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Use of the chi-square test with low expected value

I have a question about the use of the chi-square test. I've been told that use of the chi-squared test for independence requires that most of the expected values be over 5. What is worrying is that the expected values in my experiment are 2 -…
Ayesha
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Finding error variance and confidence interval

Two new types of petrol, called premium and super, are introduced in the market, and their manufacturers claim that they give extra mileage. Following data were obtained on extra mileage which is defined as actual mileage minus 10. Data on Extra…
sundar nataraj
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Finding confidence interval

A random sample of $700$ units from a large consignment showed that $200$ were damaged.how can we find the $95 \%$ confidence interval for the proportion of damaged unit in the consignment.
sundar nataraj
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Power function for this test

Suppose you have a sample from a normal population with mean mu, and known variance $\sigma^2$. What is the power function for $H_0: \mu = 0$ versus $H_a: \mu \ne 0$ at $\alpha = 0.05$? Attempt: If we standardize, we get $Z= \bar{x} -…
lord12
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Bound for deviation from mean of binomial random variable

Let $S_n$ denote a binomial $(n,p)$ random variable. The problem is to show that there is a constant $C$ depending only on $p$ such that for all $\epsilon > 0,$ $$P(|S_n/n - p| > \epsilon) \le \frac{C}{n^{10} \epsilon^{20}}.$$ The hint is to use…
Mr. Chip
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Computing sample variance and error using Monte Carlo

Asked to compute estimator for the following function, $$\theta = \int_0^\infty \mathrm{e}^{-x^2}~\mathrm{d}x$$ which can be solved by transforming the limits to 0 to 1 and solving the following expectation using Monte Carlo, $$…
takeshi kovacs
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