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Let X(t) be an iid random process and hence X(t) has an
identical distribution for any t i.e., distributions are identical at instants of time t1, t2...tn, so 1st order pdfs f(x1;t1), f(x2;t2)....f(xn;tn) are time invariant and
further X(t1) and X(t2) are independent for any two different t1 and t2.
So,
f(x1, x2, . . . , xn; t1, t2, . . . , tn) = f(x1;t1)*f(x2;t2)*....*f(xn;tn)
f(x1;t1), f(x2;t2).... f(xn;tn) are time invariant, therefore their product f(x1, x2, . . . , xn; t1, t2, . . . , tn) is also time invariant which is nth order pdf. So X(t) is strict sense stationary.
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