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November 30th, 2015, 06:21 AM   #11
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Quote:
 Originally Posted by tttim I haven't learnt differentiation The derivative of x^w where x is a variable and w is a constant is wx^(w-1). The simplest example is that the derivative of x^2 is 2x. November 30th, 2015, 05:22 PM   #12
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Quote:
 Originally Posted by tttim I haven't learnt differentiation In that case, complete the square:
\displaystyle \begin{align}\hat{p}(1-\hat{p}) &= \hat{p} - \hat{p}^2 \\ &= -(\hat{p}^2 - \hat{p}) \\ &= -(\hat{p}^2 - 2\hat{p} \cdot \frac{1}{2} + (\frac{1}{2})^2) - (-(\frac{1}{2})^2) \\ &= -(\hat{p} - 0.5)^2 + 0.25 \end{align}

Then you can see that the expression is maximised when $\displaystyle \hat{p} = 0.5$. Tags confidence, interval, proportion, sample, size Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tttim Probability and Statistics 1 November 28th, 2015 02:50 PM shivadiva Advanced Statistics 0 April 30th, 2013 07:46 PM mikeportnoy Algebra 1 March 14th, 2012 12:42 PM jskrzy Algebra 1 November 16th, 2011 04:17 PM kerrymaid Advanced Statistics 1 June 11th, 2010 05:25 AM

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