STA255H1 Lecture Notes - Lecture 3: Bernoulli Trial, Binomial Distribution, Bernoulli Distribution
Document Summary
The distribution of a variable tells us what values it takes and how often it takes these values. A random variable y is said to be discrete if it assumes only a finite or countable number of distinct values. The probability distribution of y lists the values and their probabilities: Probability : (cid:1868)(cid:2869), (cid:1868)(cid:2870), (cid:1868)(cid:2871), probabilities of all points in s that are assigned the value y. The probability that y takes on the value y, (cid:4666)=(cid:4667), is defined as the sum of the. (cid:1868)(cid:4666)(cid:4667)=(cid:4666)=(cid:4667) is called a probability function for y. The probability distribution for y can be described by a formula, a table, or a graph that provides p(y) for all y. i. e. if. Theorem: for any discrete probability function, p(y): (cid:882) (cid:1868)(cid:4666)(cid:4667) (cid:883) for all y, (cid:1868)(cid:4666)(cid:4667) Probability : (cid:1868)(cid:2869), (cid:1868)(cid:2870), (cid:1868)(cid:2871), : (cid:882) (cid:1868) (cid:883) for each =(cid:883),(cid:884),(cid:885), , (cid:1868)(cid:2869)+ (cid:1868)(cid:2870)+ (cid:1868)(cid:2871)+ =(cid:883).
