Tutorial3_ans - EE 3008. Random Process Tutorial Solutions...

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EE 3008. Random Process Tutorial Solutions Q1) All possible outcomes are listed below, HHH HHT HTH HTT THH THT TTH TTT There three events with two heads and one tail, i.e., HHT HTH THH Therefore the probability is 3/8. Q2) Pr{ . / } ( ) . . . 05 3 4 2 3 4 5 16 0 5 3/4 2 2 0 5 << = = = −= ∫∫ xf x d x x d x () Pr{ . . } ( ) . . . .. −< < = = = = 2 0 025 0 5 2 0 x f x dx xdx Q3) 4 22 1 4 2 2 2 2 1 11 4 1 2 . 5 33 2 1 var( ) ( ) ( ) = ( ) 2.5 2.5 =0.75 3 EX x f xdx xdx XE X E x x f x d x x d x −∞ == = = =− = Q4) εε ε 3 0 2 2 0 2 31 2 = = AA d A A / / = Q5) 3 2 2 2 2 2 2 = = d A A A A / / / / = Q6) (a) The average bit error rate (BER) for d = 0 is 01 1 . 5 .5 0 111
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