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main.toc
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\vskip -8pt
\contentsline {schapter}{Introduction}{iii}{chapter*.2}%
\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}%
\contentsline {chapter}{\numberline {2}Axioms}{3}{chapter.2}%
\contentsline {chapter}{\numberline {3}Random Variables}{21}{chapter.3}%
\contentsline {chapter}{\numberline {4}Conditional Probability}{27}{chapter.4}%
\contentsline {chapter}{\numberline {5}Distributions}{49}{chapter.5}%
\contentsline {chapter}{\numberline {6}Random Numbers}{73}{chapter.6}%
\contentsline {section}{\numberline {6.1}Uniform Random Numbers}{73}{section.6.1}%
\contentsline {section}{\numberline {6.2}Central Limit Theorem}{80}{section.6.2}%
\contentsline {section}{\numberline {6.3}From Uniform to Other}{84}{section.6.3}%
\contentsline {section}{\numberline {6.4}Triangular Distribution}{86}{section.6.4}%
\contentsline {chapter}{\numberline {7}Maximum Likelihood Detection: BPSK}{87}{chapter.7}%
\contentsline {section}{\numberline {7.1}Maximum Likelihood}{87}{section.7.1}%
\contentsline {chapter}{\numberline {8}Transformation of Random Variables}{89}{chapter.8}%
\contentsline {section}{\numberline {8.1}Gaussian to Other}{89}{section.8.1}%
\contentsline {section}{\numberline {8.2}Conditional Probability}{90}{section.8.2}%
\contentsline {chapter}{\numberline {9}Bivariate Random Variables: FSK}{91}{chapter.9}%
\contentsline {section}{\numberline {9.1}Two Dimensions}{91}{section.9.1}%
\contentsline {chapter}{\numberline {10}Exercises}{93}{chapter.10}%
\contentsline {section}{\numberline {10.1}BPSK}{93}{section.10.1}%
\contentsline {section}{\numberline {10.2}Coherent BFSK}{96}{section.10.2}%
\contentsline {section}{\numberline {10.3}QPSK}{98}{section.10.3}%
\contentsline {section}{\numberline {10.4}$M$-PSK}{99}{section.10.4}%
\contentsline {section}{\numberline {10.5}Noncoherent BFSK}{100}{section.10.5}%
\contentsline {section}{\numberline {10.6}Craig's Formula and MGF}{104}{section.10.6}%
\contentsline {chapter}{\numberline {A} Axioms }{107}{appendix.A}%
\contentsline {section}{\numberline {A.1}Definitions}{107}{section.A.1}%
\contentsline {section}{\numberline {A.2}Boolean Logic}{108}{section.A.2}%
\contentsline {section}{\numberline {A.3}Properties}{109}{section.A.3}%
\contentsline {chapter}{\numberline {B} Z-transform}{111}{appendix.B}%
\contentsline {chapter}{\numberline {C}Distributions}{113}{appendix.C}%
\contentsline {section}{\numberline {C.1}Bernoulli }{113}{section.C.1}%
\contentsline {section}{\numberline {C.2}Binomial Distribution}{115}{section.C.2}%
\contentsline {section}{\numberline {C.3}Uniform Distribution}{118}{section.C.3}%
\contentsline {section}{\numberline {C.4}Triangular Distribution}{120}{section.C.4}%
\contentsline {chapter}{\numberline {D}Identities}{127}{appendix.D}%