GE 331-Lecture 3

GE 331-Lecture 3 - Summary Counting Permutations of k...

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IE 300/GE 331 Lecture 3 Negar Kiyavash, UIUC 1 Summary Counting • Permutations of k elements out of n different elements: •T h e number of combination of k elements out of n different elements: • Partitions: no. of permutations of n=n 1 +…+n k objects of which n 1 are of type 1, …, n k are of type k: )! /( ! ) 1 ( ... ) 1 ( k n n r n n n P n k = + × × × = ) ! ! ! /( ! 2 1 k n n n n L ) )! ( ! /( ! k n k n
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IE 300/GE 331 Lecture 3 Negar Kiyavash, UIUC 2 • What are the definitions of outcome and event for a random experiment (trial)? • After a random experiment how many outcomes occur? How many events occur? Only one outcome, but many events. • Is the notion of probability related to the events or out comes? • Both. See the next slide.
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IE 300/GE 331 Lecture 3 Negar Kiyavash, UIUC 3 Equalikely Events • Probability of an event A occurring M times in a sample space of size N: P(A)= M/N • Probability of an event depends on the event via M and on the outcome via the size of sample space N • Example: Flip a coin twice: • A={see a H at least once} P(A)=size A/size =3/4 )} , ( ), , ( ), , ( ), , {( T T H T T H H H = Ω
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IE 300/GE 331 Lecture 3 Negar Kiyavash, UIUC 4 Size of Sample Space • An urn has n balls; m of which are red. We draw k balls without replacement. What is the probability that i of them are red?
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GE 331-Lecture 3 - Summary Counting Permutations of k...

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