JointDist-4 - The Questions of Our Time Life Gives You...

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1 The Questions of Our Time Y is a non-negative continuous random variable Probability Density Function: f Y ( y ) Already knew that: But, did you know that: ?!? No, I didn’t think so... Analogously, in the discrete case, where X = 1, 2, …, n dy y f y Y E Y ) ( ] [ dy y Y P Y E 0 ) ( ] [ n i i X P X E 1 ) ( ] [ Life Gives You Lemmas, Make Lemma-nade! A lemma in the home or office is a good thing Proof: dy y Y P Y E 0 ) ( ] [ dy y F 0 )) ( 1 ( y ) ( y F ] [ Y E   0 0 ) ( ) ( y y x Y y dy dx x f dy y Y P y x ] [ ) ( ) ( 0 0 0 Y E dx x f x dx x f dy x Y x Y x y Discrete Joint Mass Functions For two discrete random variables X and Y , the Joint Probability Mass Function is: Marginal distributions: Example: X = value of die D 1 , Y = value of die D 2 ) , ( ) , ( , b Y a X P b a p Y X y Y X X y a p a X P a p ) , ( ) ( ) ( , x Y X Y b x p b Y P b p ) , ( ) ( ) ( , 6 1 36 1 6 1 6 1 , ) , 1 ( ) 1 ( y y Y X y p X P Consider households in Silicon Valley A household has C computers: C = X Macs + Y PCs Assume each computer equally likely to be Mac or PC A Computer (or Three) in Every House 3 32 . 0
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