0

Why does iid (independent and identically distributed) have same probability distribution. What does it implies.

Akshit Arora
  • 1
  • 2
    Have you tried searching the site, e.g. https://stats.stackexchange.com/questions/99126/are-random-sample-and-iid-random-variable-synonyms or https://stats.stackexchange.com/questions/213464/on-the-importance-of-the-i-i-d-assumption-in-statistical-learning ? – Tim Sep 25 '17 at 20:37

1 Answers1

0

Let us consider a simple example: imagine we flip a coin several times. Let the random variable $Y_n = 1$ if trial $n$ is heads, $Y_n=0$ otherwise.

$Y_i$ and $Y_j$ are independent as the result of trial $j$ does not depend at all of the result of trial $i$.

As we repeat same experiment, we say that $Y_i$ identically distributed. We have same probability to observe heads $ P(Y_i=1)=P(Y_j=1)$ (and obviously tails $P(Y_i=0)=P(Y_j=0))$.

Razvan Ionescu
  • 1
  • 1