answersLogoWhite

0

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.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao
MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
EzraEzra
Faith is not about having all the answers, but learning to ask the right questions.
Chat with Ezra

Add your answer:

Earn +20 pts
Q: Why iid random process is stationary?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Statistics

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.

Trending Questions
Explain the meaning what percentiles from the National Center for Health Statistics source The 95th percentile of the length of newborn females is 53 8cm? What is the probability that the dealer will not get blackjack? What is the probability that a person chosen at random was born on a Saturday or Sunday? What is the probability of drawing either the ace of spades or a heart from a standard deck of playing cards? How many drams in 40000 tons? How many red 2's are in a deck of cards? Two coins and one six sided cube are tossed together What is the probability of getting 2 heads and a four? What percentage of data values of a normal distribution will fall within one standard deviation below the mean? Which status level used on a SITREP is defined as full strength 90 percent or more for fit duty? How many three digit numbers have three distinct digits? What is the estimated number of Christians in the US? How many possibilities are there with the four digit numbers 0000-9999 while the first number cannot be 0 or 9? What is the median mode and mean for 95 88 79 92 78 88 93 100 69 98? How often do the highest CD rates change? How important is statistics in medicine? How long does it take in college to become an actuary? On average how long does it take to get pregnant if you are 32? Between billion or million which is greater? Of the students in Miss Jones class 8 have blond hair 10 have brown hair 5 have red hair 6 have black hair and 1 has purple hair What is the probability that a student selected at random will? A Under equilibrium conditions and T 0 K what is the probability of an electron state being occupied if it is located at the fermi level?