Data 605 - Week9 HW

Question 11

Question 2

$$ g(t) = {j=0}^n e^{tj} {{n}}p^jq{n-j} \ g(t) = {j=0}^n {{n}}(pe^t)jq^{n-j} \ g(t) = (pe^t+q)n \

g’(t) = n(pe^t+q){n-1}pe^t \ g’‘(t) = n(n-1)(pe^t+q)(pet)^2 + n(pe^t+q)npe^t \ g’(0) = n(p+q)^{n-1}p =np \

g’‘(0) = n(n-1)(p+q)^{n-1}p2 + n(p+q)^np \ g’’(0) = n(n-1)p^2 + np \

\

^2 = _2-_1^2 = g’‘(0) - g’(0)^2 \ ^2 = n(n-1)p^2 + np - (np)^2 \ ^2 = np[(n-1)p +1 -np] \ ^2 = np[(np-p) +1 -np] \

$$

Question 3

$$ g(t) = _0^e{tx}e^{-x} dx \ g(t) = |_0^{} \ g(t) = \

g’(t) = \ g’(0) = = \

g’‘(t) = \ g’’(0) = = $$