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Is a random sample IID?
A random sample is a sequence of independent, identically distributed (IID) random variables. The term random sample is ubiquitous in mathematical statistics while the abbreviation IID is just as common in basic probability, and thus this chapter can be viewed as a bridge between the two subjects.
What are IID observations?
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.
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 an example of a random sample?
The sampling error is inevitable when sample data is being used. Unbiased random sampling results in more reliable and unbiased conclusions. For example, the employee satisfaction survey mentioned above makes use of a sample size of 85 employees.
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.
Which is a random variable associated with an event?
An indicator random variable is a special kind of random variable associated with the occurence of an event. The indicator random variable IA associated with event A has value 1 if event A occurs and has value 0 otherwise.