(New page: Let O=TTHHTHTTHT and knowing p=P[head] <math>P[O;p] = p^4(1-p)^6</math> <math>P_{ML}=max(p^4(1-p)^6)</math>) |
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<math>P_{ML}=max(p^4(1-p)^6)</math> | <math>P_{ML}=max(p^4(1-p)^6)</math> | ||
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| + | To find the max of a function one could find the derivative of the function and set the it zero and then solve for the variable that was used in finding the derivative. | ||
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| + | <math>\frac{d}{dp}(p^4(1-p)^6) = 2*p^3(p-1)^5(5p - 2)</math> | ||
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| + | <math>2*p^3(p-1)^5(5p - 2) = 0, p = 2/5</math> | ||
Revision as of 18:25, 4 November 2008
Let O=TTHHTHTTHT
and knowing p=P[head]
$ P[O;p] = p^4(1-p)^6 $
$ P_{ML}=max(p^4(1-p)^6) $
To find the max of a function one could find the derivative of the function and set the it zero and then solve for the variable that was used in finding the derivative.
$ \frac{d}{dp}(p^4(1-p)^6) = 2*p^3(p-1)^5(5p - 2) $
$ 2*p^3(p-1)^5(5p - 2) = 0, p = 2/5 $
