STA215H5 Lecture Notes - Lecture 12: Binomial Distribution, Continuous Or Discrete Variable, Sample Space
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Sta215 lecture 12: random variable real-valued function for which the domain is a sample space, ex 1. A fair die is thrown twice: the sample points are(1,1),(1,2),(1,3),,(6,6). Let us assign the same probability 1/36 for each of these points. Suppose we are interested in the sum of the numbers of each outcome. We will sometimes denote p(y=y) by p(y): the probability distribution for a discrete variable y can be represented by a formula, a table, or a graph that provides p(y) =p(y=y) for ally. Important result for any discrete probability distribution, the following must be true: 1. 0 p (y) 1 for all y: 2. Y p (y) = 1, where the summation is over all values of y with nonzero probability: ex 2. There are 8 possible arrangements of girls and boys. For example, ggb means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally likely: a.
