What is meant by IID random variable?

What is meant by IID random variable?

In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d. or iid or IID.

What does IID sample mean?

Identically Distributed
In statistics, we usually say “random sample,” but in probability it’s more common to say “IID.” Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in the sample are taken from the same probability distribution.

Why returns are better than prices?

Most financial studies involve returns, instead of prices, of assets. First, for average investors, return of an asset is a complete and scale-free summary of the investment opportunity. Second, return series are easier to handle than price series because the former have more attractive statistical properties.

How can x 1, x 2, x n be iid?

If X denote a random variable which means the “result of a coin toss” then x 1, x 2,…, x n are the results of repeated coin tossing. Are x 1, x 2,…, x n IID? If yes, how can observations be variables? Or are X 1, X 2,…, X n all considered as random variables if we want to consider them IID? How can a random sample be IID?

How are x 1, x 2 random variables independent?

If X 1, X 2, … designate the result of the 1st, 2nd, and so on toss (where X i = 1 means that in the i-th toss you have got head and X i = 0 tail), you have that X 1, X 2, … are iid. They are independent since every time you flip a coin, the previous result doesn’t influence your current result.

Which is an example of an iid random variable?

Im sure you know that iid means independent, identically distributed. I think the most prominent example is a coin toss repeated several times. If X 1, X 2, … designate the result of the 1st, 2nd, and so on toss (where X i = 1 means that in the i-th toss you have got head and X i = 0 tail), you have that X 1, X 2, … are iid.

How are probability independent, identically distributed random variables defined?

Edit: there is a mathematical definition of independence, but I don’t think it is necessary at the moment. They are identically distributed, since every time you flip a coin, the chances of getting head (or tail) are identical, no matter if its the 1st or the 100th toss (probability distribution is identical over time).