Big O Magnitude Notation: Difference between revisions

Revision as of 00:21, 29 August 2024

Like Big O Unit Notation, Big O Magnitude Notation refers to a notation used to express orders of magnitude.

A function $f(n)=O(10^{k})$ if $\exists n_{0}\in \mathbb {R+}$ such that $\forall n\geq n_{0}:10^{k}\leq f(n)<10^{k+1}$

A random variable $X=O(10^{k})$ if $P[10^{k}\leq X<10^{k+1}]=1$ .

Revision as of 00:19, 29 August 2024 edit Roshan (talk \| contribs) Bureaucrats, Interface administrators, Administrators 430 edits Created page with "Like Big O Unit Notation, Big O Magnitude Notation refers to a notation used to express orders of magnitude. == Formal Definition for Functions == A function <math>f(n) = O(10^k)</math> if <math>\exists n_0 \in \mathbb{R+}</math> such that <math>\forall n \geq n_0 : 10^k \leq f(n) < 10^{k+1}</math> == Formal Definition for Random Variables == Colloquially, one can say a random variable <math>X = O(10^k)</math> if its probability distribution function has meas..."		Revision as of 00:21, 29 August 2024 edit cin gbere le Roshan (talk \| contribs) Bureaucrats, Interface administrators, Administrators 430 edits No edit summary Newer edit →
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	== Formal Definition for Random Variables ==		== Formal Definition for Random Variables ==

	~~Colloquially, one can say a~~ random variable <math>X = O(10^k)</math> if ~~its probability distribution function has measure zero outside of~~ <math>[10^k, 10^{k+1}]</math>		A random variable <math>X = O(10^k)</math> if <math>P[10^k \leq X < 10^{k+1}] = 1</math>.