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From the way you write the information, it seems that you assume you have only one parameter to estimate ($\theta$) and you consider one random variable (the observation $X$ from the sample). This makes the argument much simpler so I will carry it in this way. You use the information when you want to conduct inference by maximizing the log likelihood. That log-likelihood is a function of $\theta$
Where does the choice of the Greek letter $\lambda$ in the name of “lambda calculus” come from? Why isn't it, for example, “rho calculus”?
I'm reading a book about Haskell, a programming language, and I came across a construct defined "algebraic data type" that looks like data WeekDay = Mon | Tue | Wed | Thu | Fri | Sat | Sun That simply declares what are the possible values for the type WeekDay. My question is what is the meaning of algebraic data type (for a mathematician) and how that maps to the programming language construct?
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What is the Fourier transform? What does it do? Why is it useful (in math, in engineering, physics, etc)? This question is based on the question of Kevin Lin, which didn't quite fit in Mathoverflow. Answers at any level of sophistication are welcome.
I came across the statement that Yoneda-lemma is a generalization of Cayley`s theorem which states, that every group is isomorphic to a group of permutations. How exactly is Yoneda-lemma a generalization of Cayley`s theorem? Can Cayley's theorem be deduced from Yoneda lemma, is it a generalization of a particular case of Yoneda, or is this instead, a philosophical statement? To me, it seems that Y
$\pi$ Pi Pi is an infinite, nonrepeating $($sic$)$ decimal - meaning that every possible number combination exists somewhere in pi. Converted into ASCII text, somewhere in that infinite string of digits is the name of every person you will ever love, the date, time and manner of your death, and the answers to all the great questions of the universe. Is this true? Does it make any sense ?
At school, I really struggled to understand the concept of imaginary numbers. My teacher told us that an imaginary number is a number that has something to do with the square root of $-1$. When I tried to calculate the square root of $-1$ on my calculator, it gave me an error. To this day I still do not understand imaginary numbers. It makes no sense to me at all. Is there someone here who totally
Sorry, but I do not understand the formal definition of "universal property" as given at Wikipedia. To make the following summary more readable I do equate "universal" with "initial" and omit the tedious details concerning duality. Suppose that $U: D \to C$ is a functor from a category $D$ to a category $C$, and let $X$ be an object of $C$. A universal morphism from $X$ to $U$ [...] consists of a
Singular value decomposition (SVD) and principal component analysis (PCA) are two eigenvalue methods used to reduce a high-dimensional data set into fewer dimensions while retaining important information. Online articles say that these methods are 'related' but never specify the exact relation. What is the intuitive relationship between PCA and SVD? As PCA uses the SVD in its calculation, clearly
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