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$\begingroup$ I prefer $\max\{f(x_1,\ldots,f(x_n)\}$ with curly braces and no parentheses. In this instance, the parentheses don't actually help, and the curly braces remind you that the thing whose maximum is sought is a set rather than a tuple. $\endgroup$
Get the range of the required distribution, in this case, max(X, Y) Find the CDF of this distribution as a function of the known distributions Find the PDF of the distribution by differentiating the CDF
21 de ago. de 2011 · $\max\{x_1,x_2\} = \cases{x_1, \text{if }x_1 > x_2\\x_2, \text{otherwise}}$ You can define like that the maximum of any finitely many elements. When the parameters are an infinite set of values, then it is implied that one of them is maximal (namely that there is a greatest one, unlike the set $\{-\frac{1}{n} | n\in\mathbb{N}\}$ where there is no greatest element)
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19 de set. de 2017 · Since composition of convex functions is convex, we only need to show max (x, y) is convex. But max (x, y) = x + y 2 + | x − y 2 | and | ⋅ | is obviously convex. A function f: Rn → R is convex if and only if its epigraph epif = {(x, t) ∈ Rn × R ∣ f(x) ≤ t} is a convex set.
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But let's take x = 2, then (1 - 2) ^ 2 will be (-1) ^2 which is nothing but 1 and according to op's max function, 1 should be returned. But since you gave the condition of x >= 1, we always return 0 even when x is something like 2. I think in comments what Andre Holzner said is correct.
it is intuitive that we can "pull out" the λ λ as the max function gets value of the image of a given function and does not "work" with scalars. But how can we say it in a formal way? If c ≥ 0 c ≥ 0 then supx ch(x) = csupx h(x) sup x c h (x) = c sup x h (x). This is obvious if c = 0 c = 0, so suppose c> 0 c> 0.
19 de fev. de 2013 · A simple proof of the triangle inequality that is complete and easy to understand (there are more cases than strictly necessary; however, my goal is clarity, not conciseness). Prove the triangle inequality $| x | + | y| ≥ | x + y|$. Without loss of generality, we need only consider the following cases: Case $1$.
Find the expected value of random variables $\max_i(X_i)$ and $\min_i(X_i)$. The sad truth is I don't have any good idea how to start and I'll be glad for a hint. probability
