Pfalse alarm p x h0 m0 x m0 p h0 m0 q pmiss

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: is 1/(2a(1 − a)). So the mean number of coin flips required to produce one Bernoulli random variable with parameter 0.5 using the biased coin by this method is 1/(a(1 − a)). 3.9. FAILURE RATE FUNCTIONS 111 u u=1 !1 F (u) X F (c) X + F (c) X ! c 0 Figure 3.23: E [X ] is the area of the + region minus the area of the − region. 3.8.3 The area rule for expectation based on the CDF There is a simple rule for determining the expectation, E [X ], of a random variable X directly from its CDF, called the area rule for expectation. See Figure 3.23, which shows an example of a CDF FX plotted as a function of c in the c − u plane. Consider the infinite strip bounded by the c axis and the horizontal line given by u = 1. Then E [X ] is the area of the region in the strip to the right of the u axis above the CDF, minus the area of the region in the strip to the left of the u axis below the CDF, as long as at least one of the two regions has finite area. The area rule can also be written as an...
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