ASDBIPAD
Posted on January 1, 2002
Tags: rawhtmldemo
1 Binomial Theorem and Probability¶
Binomial Coefficient tells us:
- Number ways to pick k-length subsets of a n-length set
- Number of k -> n functions but
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Column[Table[Binomial[n, k], {n, 0, 5}, {k, 0, n}], Center]
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Notice the distribution of {1,5,10,10,5,1} looks like a probability distribution
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Binomial[5,#1]& /@ Range[0,5]
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{1, 5, 10, 10, 5, 1}Notice sum over \(\sum_{k\in 0..n}{n \choose k}\) equals \(2^n\)
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Total[Binomial[5,#1]& /@ Range[0,5]]==Inactivate[2^5]
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ListLinePlot[Binomial[3,#1]& /@ Range[0,3] ]
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ListLinePlot[Binomial[7,#1]& /@ Range[0,7] ]
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ListLinePlot[Binomial[10,#1]& /@ Range[0,10] ]
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ListLinePlot[Binomial[15,#1]& /@ Range[0,15] ]
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ListLinePlot[Binomial[25,#1]& /@ Range[0,25] ]
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