are you sure you can differentiate w.r.t. p
this equation looks like the expectation of a geometric series which I posted at
https://www.physicsforums.com/showthread.php?t=70705
quoted from [PLAIN]www.ida.liu.se/~TDDB08/2005/slides/l5-6.pdf[/URL]
but this is not a very good reference for it.
<<<
Sheffer in 1913 provided a connective, called the Sheffer
stroke and denoded by |, which is suffcient to express any
other connective in the case the of two-valued...
a related problem is
what is the the expected number of throws to get a six on a fair dice
this was raised at
https://www.physicsforums.com/archive/topic/t-45262_The_expected_value_of_a_Geometric_Series.html
which seems to be closed now.
yes the answer is 6 but how do you prove it...
going back to which is greater a^b or b^a. ( i can't use the special symbols)
then assume a>b (without loss of generality)
then
if b=1 then a^b =a b^a =1 so a^b is greater
there are some special cases for a,b, <=3 which I leave you to find
but for all other cases
b^a is greater...