Table of Contents
Do IID random variables have same mean?
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. Which means they have the same parameters namely mean, std dev.
What does it mean for two random variables to be equal in distribution?
Two random variables X and Y are said to be equivalent, or equal in law, or equal in distribution, iff they have the same probability distribution function, Equivalently, X and Y are equal in law iff fX(x) = fY (x), ∀x ∈ R.
What is the mean of the sum of two random variables?
The mean of the sum of two random variables X and Y is the sum of their means: For example, suppose a casino offers one gambling game whose mean winnings are -$0.20 per play, and another game whose mean winnings are -$0.10 per play.
Does IID mean normal?
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 it mean for a random variable to be measurable?
Definition (Measurable random variables) A random variable is a function X : Ω → R. It is said to be measurable. w.r.t F (or we say that X is a random variable w.r.t F) if for every Borel. set B ∈ B(R)
Why should the sum of the probabilities is always equal to 1?
The sum of the probabilities of all outcomes must equal 1 . If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities. Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs.
Which probability distribution has mean and variance are equal?
In poisson distribution mean and variance are equal i.e., mean (λ) = variance (λ).
How do you find the mean of a variable?
First, multiply each possible outcome by the probability of that outcome occurring. Second, add these results together.