# Tagged Questions

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### How to find confidence interval of 0.95 in this problem?

For sample $x_1,\cdots,x_{100}$, following holds. $\sum_{k=1}^{100}x_k=400$ and $\sum_{k=1}^{100}x^2_k=2500$. Find the confidence interval of 0.95 for the population mean $m$. I've calculated the ...
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### Computation of conditional probabilities

I am aware this question might not be well formulated, but it is not very clear for me neither, so if anyone could help me explicit it... I observe many examples e_i. For each example, I compute two ...
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### Queuing Theory with Poisson Distribution

Suppose customers arrive in a one-server queue according to a Poisson distribution with rate lambda=1 (in hours). Suppose that the service times equal 1/4 hour, 1/2 hour, or one hour each with ...
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### Confidence intervals for mutliparameter fit

I am doing fits to some data and currently using mathematicas nonlinearmodel fit to generate fits and CIs, as well as doing bootstrapping for CIs for completeness. However, I would like to know how to ...
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### Variance with correlated variables

A simple question that I don't manage to solve: I can use different methods to measure a magnitude $x$. The results of these methods are correlated and have some uncertainties. Combining the results ...
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From Wikipedia The prior distribution is the distribution of the parameter(s) before any data is observed, i.e. $p(\theta \mid \alpha )$. ... The sampling distribution is the distribution of ...
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### Approximations for the Coarse Graining of the one norm difference of two probability distributions

I want to coarse grain $D(P_{1},P_{2}) = \frac{1}{2} \sum_{r}^{D} |Pr(r|1) - Pr(r|2) |$ for two distinct distributions Pr(r|0) and Pr(r|1). Such that $\sum_{r} P(r|1) = 1$ and $\sum_{r} P(r|2) = 1$. ...
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### Calculating that confidence that pairs of lightbulbs are independently illuminated.

So, you're sitting in a dark room, and on the far wall you see $n$ lightbulbs mounted above plaques numbered $1$ through $n$. There is a lightswitch on the arm of your chair. Every time you flip the ...
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### Uniform choice for Prior Distribution

My prior function is $\Phi\left(\mathbf{k}_\ell,W_\ell\right)=\frac{1}{N}\log p\left(\mathbf{k}_\ell,W_\ell\right)$ which is determined once I choose the Bayesian prior parameter likelihood ...
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### Estimating the total attendance

Suppose you do not know how many people are attending a convention, but you do know that as each person entered he was given an identification tag with a number on it. The tags are numbered serially ...
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### Why would a statistician or mathematician want to find the ratio between two maximum likelihood in a likelihood-ratio test?

Why would a statistician or mathematician want to find the ratio between two maximum likelihood function in a likelihood-ratio test? I know maximum likelihood is the maximum of the probability ...
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### What is the probability density function of $p$ in a series of coin tosses where the true $p$ is unknown?

I have a biased coin whose bias I don't know. I know a fair coin has $p=0.5$ but I don't know if that's the case of my coin. I try and estimate the coin's real $p$ value by running a sample series of ...
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### When I read the question related to two population hypothesis test, how can I decide whether the population is dependent or independent?

Hi, I am studying two population hypothesis test in statistic. I added two Photos related to the topic which include the descripion of the topics. First one is related to depended sample. Second ...
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### Maximum Likelihood Estimator for Multinomial.

Suppose that 50 measuring scales made by a machine are selected at random from the production of the machine and their lengths and widths are measured. It was found that 45 had both measurements ...
$n$ random variables or a random sample of size $n$ $\quad X_1,X_2,\ldots,X_n$ assume a particular value $\quad x_1,x_2,\ldots,x_n$ . What does it mean? The set $\quad x_1,x_2,\ldots,x_n$ ...
It's known that a sum $\mathbf S_n$ of iid random vectors $\mathbf {X_1,X_2, X_3,...X_n}$ which are $\mathbb{R^d}$ normaly distributed with covariance matrix $\Sigma$ and mean $\mathbf 0$, will ...