part9 - Probability Homework Solution #4 2.71 P[3 or more...

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1 Probability Homework Solution #4 2.71 2 100 3 0 100 99 98 2 4 [3 or more errors] 1 [2 or fewer errors] 100 1( 1 )1 0 100 99 1 (1 ) 100(1 ) ) 2 1 099985 1.5 10 kk k PP pp p k p −− = =− ⎛⎞ ⇐ = ⎜⎟ ⎝⎠ × ⎧⎫ =− − + + ⎨⎬ ⎩⎭ = × 2.75 For an individual chip, the problem that the lifetime exceeds 1 α seconds is: 1 1 1 lifetime Pe e p −⋅ ⎡⎤ >= = ⎢⎥ ⎣⎦ ± If we consider the testing of whether each chip lifetime exceeds 1 as a sequence of Bennoulli trials, then [] 10 11 1 0 5 10 5 ( ) (1 ) 0.289 k Pk e e k = ≥= = 2.82 (a) 01 (1) , 22 == (b) 00 1 10 1 21 ) ( ) ( ) 36 15 ) ( ) ( ) p np n p n p n p n += + + In matrix notation, we have [ ] 0 1 33 ) , ) ( ) , ( ) 66 pn pnpn ++ = , or ) ( ) p n + = Ρ
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2 (c) 11 (0) , 22 21 5 7 33 (1) , , 15 2 2 12 12 66 57 35 (2) , , 12 12 8 8 3 5 17 31 (3) , , 8 8 48 48 17 31 (4) , 48 48 p p p p p ⎡⎤ = ⎢⎥ ⎣⎦ == = 11 21 , 32 32 = (d) 2 (0) , (0) (2) (0) (0) p pp p p = = = P PP in general () ( 0 ) n pn p = P . To find n P , we note that if P has eigenvalues 1 λ , 2 and eigenecotrs 1 e , 2 e
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This note was uploaded on 11/29/2009 for the course EE 131A taught by Professor Lorenzelli during the Fall '08 term at UCLA.

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part9 - Probability Homework Solution #4 2.71 P[3 or more...

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