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When do random variables have the same distribution?
If you have two random variables then they are IID (independent identically distributed) if: If they are independent. As explained above independence means the occurrence of one event does not provide any information about the other event. If each random variable shares the same distribution.
What is the independence of a random variable?
If we sample repeatedly from either the Priest or Obama, then the samples are considered identically distributed. Side note: Independence also means you can multiply probabilities. Lets say the probability of heads is p, then the probability of getting two heads in a row is p*p, or p^2.
What does ” identically distributed ” mean in probability theory?
Two (real-valued) random variables $X$ and $Y$ are identically distributedif $$ P(X \\leq x) = P(Y \\leq x) $$ for all $x \\in \\mathbb{R}$. Share Cite Follow answered May 17 ’16 at 6:50
When are X and Y considered identically distributed?
If Obama and the Priest flip coins with the same probability of landing on heads, then X and Y are considered identically distributed. If we sample repeatedly from either the Priest or Obama, then the samples are considered identically distributed. Side note: Independence also means you can multiply probabilities.
We talk about independent and identically distributed variables in the context of samples. Samples are drawn from a population sequentially. And, IID relates to the values of a characteristic for the objects that you are sequentially sampling. Values for a characteristic is easy.
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.