Is IID the same as normal distribution?
If they are independent and identically distributed (IID), then they must meet the first two criteria (since differing variances constitute non-identical distributions). However, IID data need not be normally distributed. Thus, whether or not a set of data is IID is unrelated to whether they are normal.
What does IID mean in math?
Independent, identically-distributed
Independent, identically-distributed random variables We say that random variables X1, X2., Xn are independent and identically distributed (abbreviated as i.i.d.) if all the Xi are mutually independent, and they all have the same distribution. Examples: Put m balls with numbers written on them in an urn.
What is IID in communication?
We say two random variables are independent and identically distributed, abbreviated iid, if they have the same marginal pdf, and are statistically independent from each other. In digital communications, we often assume data sources produce bits which are iid.
How do you prove identical distribution?
Two variables (X,Y) are identically distributed (ID) if they have the same probability distribution. A sufficient condition for this is that CDF(X)=CDF(Y) where CDF stands for Cumulative Distribution Function. A textbook way of describing this would be to write P(x ≤ X) = P(y ≤ Y).
Why is the IID assumption needed?
So in a way the assumption of I.I.D helps simplify training machine learning algorithms by assuming that the data distribution won’t change over time or space and sample wont be dependent on each other in anyway.
What does it mean to have the same distribution?
4. Similar distribution means the type of distribution is the same. Identical distribution means the type of distribution is the same and their parameters have exactly the same value. If question stated that X and Y have same distribution then their parameters should have same values.
Why is the IID assumption important?
Does same distribution mean same variance?
The mean and variance are determined by the distribution. Thus, if they have the same distribution, they must have the same mean and variance. If two variables are iid , then they must have the same distribution.
What the IID assumption implies about the data?
What i.i.d. assumption states is that random variables are independent and identically distributed. You can formally define what does it mean, but informally it says that all the variables provide the same kind of information independently of each other (you can read also about related exchangeability).