2. You observe the number of strikes {x1, . . . , xn} scored by a bowler in n games. In each game, the bowler has a = 10

[answerhappygod]

2. You observe the number of strikes {x1, . . . , xn} scored by
a bowler in n games. In each game, the bowler has a = 10 attempts
at a strike and the probability of a strike is related to the skill
λ > 0 of the bowler as λ 1+λ . Assuming each attempt and each
game are independent, the data can be assumed to follow a Binomial
distribution i.e.: xi iid∼ Binomial a, λ 1+λ .
(a) Derive the log-likelihood as a function of λ.
(b) Derive the score as a function of λ.
(c) Derive the observed Fisher Information as a function of
λ.
(d) Show that the expected Fisher Information is E[I(λ)] = na
λ(1 + λ) 2
(e) Derive the Maximum Likelihood Estimator of λ.
(f ) Estimate the standard error of λˆ using a Normal
approximation to the likelihood, if n = 20, a = 10, x¯ = 9.15.
(g) Describe in detail how would you calculate a Jackknife
estimate of the standard error of your estimate of the skill λˆ for
the bowler? You do not need to perform the calculations.