Question

Sam has two nieces (Amy and Tina) who are fighting over a chocolate bar. Assume that the chocolate bar has length 1 foot(!). Sam decides to split the chocolate bar for the nieces. He splits it at a uniform location U on the bar namely the density of U is given by fu (u) 0 u 1 = 1, Sam fixes a number p in (0,1) and tells Amy she will get the portion of the bar that contains p. Find the expected length of the piece that Amy gets. What is the value of p that maximizes the expected length?

Answer 1

Sonu N=1 oNLI Now, P san either be on left of u or right of u Let x denote the length of the piece that any gets x=1-1 it pol Now. P/P>N) = (1-1) x=0 iv PSN P(PSN) = N :.E(X) = (2-0).P(PN) + N.P(PU) = (1-w). (1-1) + W. V = 212-20 +1 - piece that per the an any W E(X) = 0 & YN-2=0 ) N=0.5 P= Umorew P=0.5 maximizes the expected length. gets