# lec11 - Compound p.m.f 1st processor 4001 4002 450 x x x x...

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Compound p.m.f. Motivation: Real problems very seldom concern a single random variable. As soon as more than 1 variable is involved it is not suﬃcient to think of modeling them only individually - their joint behavior is important. 2 variables case: Consider the two variables: X,Y are two discrete variables. The joint probability mass function is deFned as p ( x, y ):= P X = x Y y ) Example: A box contains 5 unmarked PowerPC G4 processors of di±erent speeds: 2 400 mHz 1 450 mHz 500 mHz Select two processors out of the box (without replacement) and let = speed of the Frst selected processor = speed of the second selected processor Example (Cont’d) Summary: ²or a sample space we can draw a table of all the possible combinations of processors. We will distinguish between processors of the same speed by using the subscripts 1 and 2 1st processor Ω 400 450 500 - xxx x-x xx 2nd processor xx-xx xxx-x In total we have 5 · 4=20 possible combinations. Since we draw at random, we assume that each of the above combinations is equally likely. This yields the following probability mass function: Probabilities: mHz 0.1 0.2 1st proc. 0.0 Question 1: What is the probability for ? This might be important if we wanted to match the chips to assemble a dual processor machine Solution: )= (400 , 400) + (450 450) + (500 500) =0 . 1+0+0 1=0 3 Marginal p.m.f. Question 2: X>Y

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lec11 - Compound p.m.f 1st processor 4001 4002 450 x x x x...

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