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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Empirical Quantile Comparison Effect Size

I'm trying to recreate the following integral with empirical data: $$ \int_0^1 |F(G^{-1}(p))-p| + |G(F^{-1}(p))-p| dp $$ where $F$, $G$ are cdfs and $F^{-1}$, $G^{-1}$ are quantile functions. Here's my code in python: def eqces(u,v): import…
alanlujan91
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estimating standard deviation from data

Suppose results $x_1,x_2,x_3$ of an experiment are values of a random variable X with an unknown variance $\sigma^2.$ What is the best approximation of $\sigma^2$? D. Luenberger mentiones in "Investment Science" that the best approximation of…
student
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Did I prove this statistics question correctly?

The question is Suppose A and B are two independent and disjoint events. Suppose P{B} = 1/2. What is P{A}? Prove your answer My attempted solution: Since they are independent then P{AB} = P{A}P{B}, Now since they are also disjoint we must satisfy…
Andy
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Logit function and probability

I was reading a paper regarding using a logistic regression to predict an outcome of interest. In the paper the logit is given as logit(p) = log[p/1-p] = b0 + b1*x1 + .... + bn*xn => Which is fine but then p is given as p = 1/exp[-(b0 + b1*x1 + ....…
riderchap
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What CI should I use when finding Margin of Error?

I've begun an assignment where I collect my own data. The assignment is now asking me to find margin of error with the collected data. I have nearly everything I need for the equation with the exception of the Confidence Interval. Do you think it…
user84823
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How do I adjust values for consistency?

What's a fair way to adjust value for consistency? For example, Machine A pumps out 10 lollipops every day. Machine B pumps out 0 lollipops one day and 20 lollipops the next, which averages 10 lollipops a day (you just don't know when you'll get 0…
Bradford
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Help with this chi square stats problem?

I'm presented with: A rivet is to be inserted into a hole. If the standard deviation of hole diameter exceeds 0.02 mm, there is an unacceptably high probability that the rivet will not fit. A random sample of n = 15 parts is selected, and the…
rphello101
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Stats and Probability question

Find the probability of being dealt a bridge hand of 13 cards containing 5 spades, 2 hearts, 3 diamonds, and 3 clubs.
Danathon
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What is the estimator of $P(X=0)$ for $X\sim\operatorname{Poisson}$

Let $X\sim\operatorname{Poisson}$. What is the estimator of $P(X=0)$ by maximum likelihood method. If it based on random sample of size $n$ Thank you
user99853
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Why does this alternative hypothesis test make a better statement vs the other?

I have a problem that is asking me to just set up a hypothesis test. Here is the background of the question: Suppose that the specificataions state that mean strength of welds should exceed $100$ $lb/in^2$; the inspection team decides to test $H_0:…
TheHopefulActuary
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Show these two are the same (statistics)

Show that $$\sum_{i=0}^n(x_i-\bar x)^2=\sum_{i=0}^n(x_i-\bar x)x_i$$ This is what I have done. Expanded the square $$\sum_{i=0}^n(x_i-\bar x)^2=\sum_{i=0}^n(x_i-\bar x)\times\sum_{i=0}^n(x_i-\bar x)$$ Not sure how to continue...
user95087
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normal approximation to binomial and poisson

My lecturer said that the following approximations are best when normal approximation to the binomial is best when np$\ge$5 and n(1-p)$\ge$5 normal approximation to the poisson when $\lambda$>20 poisson approximation to the binomial when n is…
clarkson
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How do I find a confidence interval when I am trying to determine the mean number of events per unit of time?

Let's say that I want to estimate the number of cars that pass my house every minute. I count 30 cars in 10 minutes, and I want to use this to generate a confidence interval. How should I do this? The point estimate would be 3 cars/minute, but I…
PhiNotPi
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How to find correlation coefficient given joint distribution

Random variables $X$ and $Y$ follow a joint distribution $$f(x, y) = \left\{ \begin{array}{ll} 2,& 0 < x \leq y < 1,\\ 0,&\text{otherwise}\end{array}\right. $$ Determine the correlation coefficient between $X$ and $Y$ .
Danathon
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Mean of a random variable

Two tire-quality experts examine stacks of tires and assign a quality rating to each tire on a 3-point scale. Let X denote the rating given by expert A and Y denote the rating given by B. The following table gives the joint distribution for X and Y…
Danathon
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