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Conditional Optimization

• To: mathgroup at smc.vnet.net
• Subject: [mg80910] Conditional Optimization
• From: John <jwa0 at lehigh.edu>
• Date: Wed, 5 Sep 2007 02:55:35 -0400 (EDT)

Problem:

 Find the largest value of n for which BetaRegularized[1-p0,n-c,c
+1]>=1-alpha.

 Find the smallest value of n for which BetaRegularized[1-p1,n-c,c
+1]<=beta.

0<p0<p1<1, 0<alpha<1, 0<beta<1, c is a positive integer.

Values of p0, p1, alpha, beta and c are specified.

Since BetaRegularized[1-p0, n-c,c+1] decreases as n increases, the
required value of n satisfies the equation, BetaRegularized[1-p0,n-c,c
+1]=1-alpha.

Since BetaRegularized[1-p1, n-c,c+1] decreases as n increases, the
required value of n satisfies
the equation, BetaRegularized[1-p1,n-c,c+1]=beta.

My attempts to use Solve to find the required values of n were
unsuccessful. Hints or suggestions would be appreciated.

John