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2 years ago

MA2102

Probability and Statistics

Lecture-20

In general , probability distribution of k−k- dimensional random vector X‾≡(X1,X2,...,Xk)\underline{X}\equiv(X_1,X_2,...,X_k) is a function PX‾:Bk→RP^{\underline{X}}:\mathscr{B}_k\to \mathbb{R},

PX‾(B)=P(X‾∈B)=P({ω∈Ω:(X1(ω),X2(ω),...,Xk(ω))∈B})P^{\underline{X}}(B)=P(\underline{X}\in B)=P(\{\omega\in\Omega:(X_1(\omega),X_2(\omega),...,X_k(\omega))\in B\}) for B∈BkB\in \mathscr{B}_k

Here PX‾P^{\underline{X}} will satisfies three axioms of probability.And PX‾P^{\underline{X}} is called probability distribution of k−k- dimensional random vector X‾≡(X1,X2,...,Xk)\underline{X}\equiv(X_1,X_2,...,X_k)