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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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What is a iid sampling?
This is an abbreviation for independent and identically distributed. In the mathematical analysis of samples, it is convenient to state that each data value in the sample is a iid random variable. See related link.
What is the most random name?
Any name is just as random as every other, except where human bias is involved in the selection process.
What is the definition of the stochastic process?
The definition to the term "Stochastic Process" is: A statistical process involving a number of random variables depending on a number variable. Which in most cases, is time.
When all the items in a population have an equal chance of being selected for a sample the process is called?
random.
What is the meaning of random variable in probability distribution?
It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.It is a variable that can take a number of different values. The probability that it takes a value in any given range is determined by a random process and the value of that probability is given by the probability distribution function.
