12_DiscreteRVs-4_Joint_PMFs_packed

12_DiscreteRVs-4_Joint_PMFs_packed

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Unformatted text preview: 4/45 6/45 2/45 2 3 Let A = {S ≠ 3} (a)  Find pS(s) 1 r ⎧12 / 45, if s = 1 ⎪ ⎪18 / 45, if s = 2 pS ( s) = ⎨ ⎪15 / 45, if s = 3 ⎪ 0, otherwise ⎩ Ilya Pollak Example s Joint PMF pR,S(r,s) 3 6/45 9/45 0 2 6/45 9/45 3/45 1 4/45 6/45 2/45 2 3 Let A = {S ≠ 3} (a)  Find pS(s) and pS|A(s). 1 r ⎧12 / 45, if s = 1 ⎪ ⎪18 / 45, if s = 2 pS ( s) = ⎨ ⎪15 / 45, if s = 3 ⎪ 0, otherwise ⎩ P( A) = pS (1) + pS (2 ) = 12 / 45 + 18 / 45 = 30 / 45 Ilya Pollak Example s Joint PMF pR,S(r,s) 3 6/45 9/45 0 2 6/45 9/45 3/45 1 4/45 6/45 2/45 2 3 Let A = {S ≠ 3} (a)  Find pS(s) and pS|A(s). 1 r ⎧12 / 45, if s = 1 ⎪ ⎪18 / 45, if s = 2 pS ( s) = ⎨ ⎪15 / 45, if s = 3 ⎪ 0, otherwise ⎩ P( A) = 12 / 45 + 18 / 45 = 30 / 45 ⎧ 12 / 45 12 ⎪ 30 / 45 = 30 , if s = 1 ⎪ 18 / 45 18 pS | A ( s) = ⎨ = , if s = 2 ⎪ 30 / 45 30 ⎪ 0, otherwise ⎩ Ilya Pollak Example s Joint PMF pR,S(r,s) 3 6/45 9/45 6/45 9/45 3/45 1 4/45 6/45 2/45 2 3 (b) Find pR,Y(r,y) 0 2 Let Y = R − S 1 y Joint PMF pR,Y(r,y) 2 r 0 0 2/45 1 0 6/45 3/45 0 4/45 9/45 0 -1 6/45 9/45 0 -2 6/45 0 0 1 2 3 r Ilya Pollak Example s Joint PMF pR,S(r,s) 3 6/45 9/45 0 2 6/45 9/45 3/45 1 4/45 6/45 2/45 2 Let A = {S ≠ 3}, X = R + S 3 1 X=2 (c) Find pX|A(x). Event A P(A)=30/45 r X=3 X=4 X=5 ⎧ 4 / 45 4 = , if x = 2 ⎪ 30 / 45 30 ⎪ 6 / 45 + 6 / 45 12 = , if x = 3 ⎪ 30 ⎪ 30 / 45 ⎪ pX | A ( x ) = ⎨ 2 / 45 + 9 / 45 = 11 , if x = 4 ⎪ 30 / 45 30 ⎪ 3 / 45 3 ⎪ = , if x = 5 ⎪ 30 / 45 30 ⎪0, otherwise ⎩ Ilya Pollak...
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This note was uploaded on 09/11/2013 for the course ECE 302 taught by Professor Gelfand during the Fall '08 term at Purdue University-West Lafayette.

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