EE131A TA Recitation 4

EE131A TA Recitation 4 - EE131A Probability TA Recitation 4...

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EE131A Probability TA Recitation 4 Chihkai Chen [email protected] Office hours: Monday, 9:15-10:15pm Tuesday, 9:15-10:15pm
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Discrete R.V. Bernoulli trial Perform an experiment once and noting whether a particular event A occurs. ( p=P(A) ) Binomial Let k be the # of successes in n independent Bernoulli trials, then the probabilities of k are given by Poisson RV and Binomial RV When n>> np >> p; then for λ =np () ( 1 ) kn k n Pk p p k ⎛⎞ =− ⎜⎟ ⎝⎠ ( 1 ) ! k nk n k k e C p p k λ
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Gaussian RV Gaussian RV X~N( μ , σ ) Q-function For any X~N( μ , σ ); 2 - 2 1 () ( ) 2 1 ( ) x t Qx d t PX x Q x e π == > −= 2 2 -( - ) 2 1 , - 2 x fx x e μ σ πσ = ∞< <∞ ( ) ( ' ) ( ) Xa a a PX a P PX Q μμ σσ −− > = >= =>X~N(0,1) Q(a- μ / σ ) standardize( normalize)
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Ex. Show that if A and B are independent events, then A and B c , A c and B, and A c and B c , are also independent. A B A B c () ( ) ( ) ( ) - ( ) ( ) ( )(1 ( )) ( ) ( ) C C PA B PA PA B PA PAPB PA PB PAPB ∩= −∩ = =− = => A and B c are indep.
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This note was uploaded on 04/01/2011 for the course EECS 131 taught by Professor Jung during the Spring '11 term at CSU Channel Islands.

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EE131A TA Recitation 4 - EE131A Probability TA Recitation 4...

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