View source for Joshua Long 8.3 ECE302Fall2008sanghavi - Rhea

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>

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.

<math>\frac{d}{dp}(p^4(1-p)^6) = 2p^3(p-1)^5(5p - 2)</math>

<math>2*p^3(p-1)^5(5p - 2) = 0, p = 2/5</math>