Hi All,
Feel free to use sage/mathematica/whatever to do any math on any of the homework. Here are some hints for problem 6.
Sarah
Sage:
Either download sage or go to this link to run sage in your browser
u=var('u')
p=var('p')
k=var('k')
gdoubleprime = diff(diff( p^k/(1-(1-p)*u)^k, u),u).subs(u=1).simplify()
This gives you g''(1). Do the same to get g'(1). Then calculate the variance.
WolframAlpha:
To get g' you can type the following at wolframalpha
diff( p^k/(1-(1-p)*u)^k, u)
substitute in u=1 to get g'(1)
Then do the same for g'', etc.