If pX 1 pX 2 then the random process Xn must be stationary

If p_X [1] = p_X [2], then the random process X[n] must be stationary. True False

Solution

the given statement is TRUE by the definition of stationary random processes.

A stationary random process is defined as the process in which the probabilities of an event remains same irrelevant of when the event occurs.

i.e.,

p _ x1 = p_x2

and the above equation implies the probability of random process X[n] is same (stationary) irrespective of the dynamic shift in T ( i.e, x1 and x2)

given statement is true