01:220:322 Lecture Notes - Lecture 4: Random Variable, Standard Deviation, Expected Value
Document Summary
A random variable x (assume from now on that x is a discrete rv) has a probability distribution function f(x) where (cid:1) (cid:1) Let x be the set of all possible values of x. Then the probability distribution function, f, is defined (cid:1) (cid:1) tossed. For example, consider the case of a die. Let x be the number showing after the die is (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) (cid:1) Definition: rth moment of a rvthe rth moment of a random variable is r=1: first moment . This is called the expected value or mean of x. Equal to long-run average of many repeated trials. Indicates central location of random variable. r=2: raw second moment: we prefer to deal with the central second moment . 2 = var (x) = e((x e(x))2)
