Question

How to express a random signal mathematically? (Topic: Deterministic and Random Signal)

Answer 1

Random Process or Stochastic process are deals with trandomly varing time wave forms. Arandom process is a function of elements of sample space (s) and time(t). it is denoted by X(t,s) or simply X(t).

X(t,s) represent a family of functions by varing t and s called Ensemble. each member time function in this family is called sample function.

this random process represents a single time function when s is fixed and t is variable. it is denoted by x(t) random signal.if fixed s is si then the time functions are X(t,s_i) = x_i(t)