1 Graphs and Trees The following two definitions of a tree are equivalent Definition 1: A tree is an acyclic graph of n vertices that has n-1 edges Definition 2: A tree is a connected graph such that Vu, v E V, there is a unique path connecting u to u. In general, when we want to show the equivalence of two definitions, we must show
Discount model is in terms of conditional moments The first order condition is,u'( BE, [u'(c )x 1] The expectation is conditional expectation on investor's time t information; The basic pricing equation is P, =E, (m +1X1+)
National Motto of the United States In God We Trust The phrase derives from the line \And this be our motto. 'In God is our trust, \in the battle song that later became the U.S. national anthem, \The Star-Spangled Banner. \The phrase first appeared on U. S. coins in 1864 and became