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Do IID random variables have the same mean?
If two variables are iid , then they must have the same distribution. Which means they have the same parameters namely mean, std dev. The mean and variance are determined by the distribution. Thus, if they have the same distribution, they must have the same mean and variance.
How are random variables said to be independent?
Such random variables are also said to be independent and identically distributed, abbreviated i.i.d. We refer to the number n of random variables as the sample size. But one of the other statistics book I have says: In a Random Sampling, we guarantee that every individual unit in the population gets an equal chance (probability) of being selected.
What’s the difference between a random variable and a function?
A random sample is to randomly take a sample from a population, whereas a random variable is like a function that maps the set of all possible outcomes of an experiment to a real number. However, say if I draw some samples X 1, X 2, X 3 and X i ∼ N (μ, σ 2), where μ and σ are unknown, are X 1, X 2, X 3 random samples or random variables?
Which is a random sample according to the second definition?
So each s i is a random sample according to the second definition. Roughly, it is not an i.i.d. random sample because individuals are not random variables: you can consistently estimate E [ X] by a sample mean but will never know its exact value, but you can know the exact population mean if n = N (let me repeat: roughly.) 1
When do you use sample of random variables?
The sample of random variables has been popular in the discipline of psychometry. Generally, it is used with reference to reliability Or validity estimate and for a factor analysis. The psychometry are interested in establishing equivalence of tests for a domain. The iid concept appears to originate from linear algebra.