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Question 2 12 Marks) a) Prove that for a Gaussian (normal) random variable, X, with mean ps and variance o J2 Pr(x>= Q2 Fam n
b) Pr(X>4) @r4- 3 Ix-8>5 e) Prx-8>5) Fx1-3)- Fr(+12 1X 5+8 13 -3 3-4 3-Q12 =>1-2 13-4 3 2C13-4 3 3
Question 2 12 Marks) a) Prove that for a Gaussian (normal) random variable, X, with mean ps and variance o J2 Pr(x>= Q2 Fam nct edr Yinow hat J Note: Q) X As we Sure then x m r X 2 a-r Ox- 2 2 (X- a) X X-a b) A Gaussian random variable has a PDF of the form fr(x)= 3 2 2 x-3 Write each of the followings in terms of Q-function (with positive argument). cof (X a) Pr(X
b) Pr(X>4) @r4- 3 Ix-8>5 e) Prx-8>5) Fx1-3)- Fr(+12 1X 5+8 13 -3 3-4 3-Q12 =>1-2 13-4 3 2C13-4 3 3
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Fer rand Am vari alele 2 07 e New P (x dt t-per Let dp dt P47) ITT & PROVED. 4ENCE Given (b3 3 2 Bn rith &band arel up on lom

PCxe6) 1-fx6) 6-47 1-& ( Guwt trm p싸 a) FB 3 1-l2 P 74) &(4) PCx-ESs)+ Px-]<-6] Pla7 13)P(x3) P7 13) 1- P> 3) (s<(8-d c) : 1+

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