Isye 2027

# Here we model the observed data by a discrete type

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ity can be applied to calculate the probability of an event, if there is a partition of the sample space. The law of total probability can also be used to compute the mean of a random variable. The conditional mean of a discrete-type random variable X given an event A is deﬁned the same way as the original unconditional mean, but using the conditional pmf: E [X |A] = ui P (X = ui |A), i and also the conditional version of LOTUS holds: E [g (X )|A] = g (ui )P (X = ui |A). i The law of total probability extends from probabilities to conditional expectations as follows. If E1 , . . . , EJ is a partition of the sample space, and X is a random variable, J E [X |Ej ]P (Ej ). E [X ] = j =1 Example 2.10.4 Let 0 < p < 0.5. Suppose there are two biased coins. The ﬁrst coin shows heads with probability p and the second coin shows heads with probability q , where q = 1 − p. Consider the following two stage experiment. First, select one of the two coins at random, with each coin being selected with probability one...
View Full Document

## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

Ask a homework question - tutors are online