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For a countable set of n disjoint events E_1, E_2, ..., E_n P( union _(i=1)^nE_i)=sum_(i=1)^nP(E_i).

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

A set function mu is said to possess countable subadditivity if, given any countable disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...

Given n sets of variates denoted {X_1}, ..., {X_n} , the first-order covariance matrix is defined by V_(ij)=cov(x_i,x_j)=<(x_i-mu_i)(x_j-mu_j)>, where mu_i is the mean. ...

A functor F is called covariant if it preserves the directions of arrows, i.e., every arrow f:A-->B is mapped to an arrow F(f):F(A)-->F(B).

A covariant tensor of rank 1, more commonly called a one-form (or "bra").

The covercosine, also called the coversed cosine, is a little-used trigonometric function defined by covercos(z) = vercos(1/2pi-z) (1) = 1+sinz, (2) where vercosz is the ...

Suppose that X^~,X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~,p) is said to be a covering space of X if p:X^~->X is a surjective ...