Question

Distinguish between terms random variable and random process and random vector

Answer 1

A (real-valued) random variable is a real-valued function defined on
Ω with a technical condition (to be stated)
Common to use upper-case letters. E.g., a random variable X is a
function X : Ω → R. Y, Z, U, V, Θ, ···
Also common: random variable may take on values only in some
subset ΩX ⊂ R (sometimes called the alphabet of X, AX and X also
common notations)
Intuition: Randomness is in experiment, which produces outcome ω
according to probability P ⇒ random variable outcome is
X(ω) ∈ ΩX ⊂ R.

Random vectors and random processes
A finite collection of random variables (defined on a common
probability space (Ω,F , P) is a random vector
E.g., (X, Y), (X0, X1, ··· , Xk−1)
An infinite collection of random variables (defined on a common
probability space) is a random process
E.g., {Xn, n = 0, 1, 2, ···}, {X(t); t ∈ (−∞, ∞)}
So theory of random vectors and random processes mostly boils
down to theory of random variables.

Answer 2

Answer:

Xplease explain it more

Step-by-step explanation: