Nov 11, 2018 · The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v.$$ I wonder if anyone has a clever mnemonic for the above formula. What I often do is to derive it from the Product R...

Apr 25, 2017 · To calculate the expected value, we're going to need the density function for Y. To get that, we're going to need the distribution function for Y. Let's start there. By definition, F(y) = P(Y ≤ y) = 1 − P(Y> y) = 1 − P(min(X1, …,Xn)> y). Of course, min(X1, …Xn)> y exactly when Xi> y for all i. Since these variables are i.i.d., we have F(y) = 1 − P(X1> y)P(X2> y) … P(Xn> y) = 1 ...

Jan 29, 2015 · Wikipedia states: "The unitary group U(n) U (n) is a real Lie group of dimension n2 n 2. " There seem to be two typos: one, unitary matrices are complex. So it should be a statement about complex Lie group. The other typo is n2 n 2: n2 n 2 is the dimension of GLn G L n and U(n) U (n) is a proper subgroup so clearly its dimension must be smaller than n2 n 2. What's the dimension of U(n) U (n)?

Epsilon is used in mathematics to denote an arbitrarily small positive quantity or a small positive number in calculus and analysis.

Oct 20, 2021 · hence the series converges to 1. This is not, however, sufficient proof of convergence. Perhaps a relation to the series ∞ ∑ n = 1 1 n2

Sep 25, 2019 · Show that surprisingly, N N and M M have the same probability distribution, and their common mean is e! This is Example 3.28 on page 124 in Ross's book (Introduction to Probability Models-11th edition) My question is that: why Pr(N> n) Pr (N> n) is Pr(U1>U2>...> Un) Pr (U 1> U 2>...> U n) but not Pr(Un>Un−1>...>U1) Pr (U n> U n − 1>...> U 1) which is 1/n! 1 / n!?

Dec 19, 2022 · $$ \\mbox{What can we say about the integral}\\quad \\int_{0}^{a} x!\\,{\\rm d}x\\ ?. $$ Or something like $\\displaystyle\\int_{0}^{3} x!\\ {\\rm d}x\\ ?$.

In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B...

May 15, 2013 · The major problem which occurs is at 70s. * The French have no word for 70, they call is 60 and 10 - soixante-dix. *So on, 71 is 60 and 11 till 79. Similarly, 80 is also not invented, it is 4 20s, quatre-vingt. 81 is 4 20s 1, quatre-vingt-un. 90 is, 4 20s 10, quatre-vingt-dix. 91 is 4 20s 11, quatre-vignt-onze. Finally, they have a word for 100 ...

John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristic...