Contents
- 1 What do you mean by identical distribution?
- 2 What does it mean for two variables to have the same distribution?
- 3 How are independent and identically distributed random variables different?
- 4 Which is the test for an identical distribution?
- 5 Which is an example of an identical and independent variable?
What do you mean by identical distribution?
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. Independent means that the sample items are all independent events. In other words, they aren’t connected to each other in any way.
What does it mean for two variables to have the same distribution?
If you (arbitrarily) choose any event E (a set of possible outcomes to which we might attribute a probability), then having the same distribution means the chance that X is in E must equal the chance that Y is in E, no matter how you chose E.
What is identically mean?
adj. 1. Being the same: another orator who used the senator’s identical words. 2. Exactly equal and alike: Your car is identical to mine.
How are independent and identically distributed random variables different?
Then “independent and identically distributed” implies that an element in the sequence is independent of the random variables that came before it. In this way, an i.i.d. sequence is different from a Markov sequence, where the probability distribution for the n th random variable is a function of the previous random variable in the sequence
Which is the test for an identical distribution?
[This distribution of Y is called a “compound distribution” in FELLER I, ch. XII.] Yet another way of testing the hypothesis that two independent groups have identical distributions is with the so-called Kolmogorov-Smirnov test. This test forms the basis of the shift function in Section 8.11.2.
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.
Which is an example of an identical and independent variable?
“Identical and independent”, any event combinations between the two dice that have the same probability. For example $P(X_1=1)$ and $P(X_3=6)$ and etc. “Identical but not independent”, any two events for one die.