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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
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...
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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.
- Spring '08
- The Land