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### What is the meaning of “All models are wrong, but some are useful”

"Essentially, all models are wrong, but some are useful." --- Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424, Wiley. ISBN 0471810339. What ...
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### In layman's terms what is the difference between a model and a distribution?

The answers (definitions) defined on Wikipedia are arguably a bit cryptic to those unfamiliar with higher mathematics/statistics. In mathematical terms, a statistical model is usually thought of as ...
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### How do you fit a Poisson distribution to table data?

I've been given a table of $x=(0,1,2,3,4,5,6)$ and $y=(3062,587,284,103,33,4,2)$, which are such that the number of $x_i$ tells an amount of children that all $y_i$s have. I'm asked to fit a Poisson ...
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### How far can be median, mode and mean be from each other and still be able to say that is a normal distribution?

I'm working on the Boston housing project of the udacity ML nano degree. A histogram of the data set looks like this: The mean, median and mode are: ...
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### Do we always assume cross entropy cost function for logistic regression solution unless stated otherwise?

I am using Matlab glmfit for logistic regression. Now I know that usually people use the cross entropy to evaluate the error in predictions against the true labels ( which different than the linear ...
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### What does it exactly mean if a random variable follows a distribution

Imagine there's a random variable such as $ε$. Then we say that $ε$ is i.i.d and follows a normal distribution with mean $0$ and variance $σ^2$. What does this mean? Is this not a variable anymore? ...
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### How to estimate the margins distribution using ecdf?

Suppose we have a random variables x. x <- rnorm(500, 2,3) Suppose that we do not know the marginal distribution of (...
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### source of statistical uncertainties

What's the source of statistical uncertainties in measurements? I understand that random noise can be a source of the uncertainty. Also sometimes the signal itself is randomly determined. In that ...
I have some questions regarding the statistical notion of "population'', the mean, standard deviation and the distribution of a population characteristic. Background: According to Wikipedia, A ...