math代写
代写math | mining代做 – 这是利用math进行训练的代写, 对math的流程进行训练解析, 涉及了math/mining等代写方面
math 170S Midterm 1 - Page 8 of 10 08/12/
- (25 points) East Empire Trading Company (EETC) would like to establish a mining chapter in the island of Solstheim, due to its rich mineral veins. However, Solstheim is a very dangerous place and together with dangers of mining, insurance becomes essential. Fortunately, EETC has an actuarial department and they have the following data for mining related claims in Solstheim.
#Claims Corresponding # Days
0 50
1 122
2 101
3 92
4+ 0
(a) (10 points) Calculate the maximum likelihood estimate for the parameter of a Pois-
son model based on the above data.
lihclihoodfumtionuN.ie =
"
########
"
i
=
365
122 +^2 ^101 +^3 ^92
– 2
=
""
,
i.^692
up-uhdihodfntionl.ly = m = -^365 +^6001 nN
- M(^2
####### "’ d)
######## "
= – 365 +
6
= 0
(^2) 600 120 = 1. 6438
Math 170S Midterm 1 – Page 9 of 10 08/12/
(b) (15 points) Calculate the Cramer-Rao lower bound. We saw in the Theorem in
page 51 of our lecture notes that MLEs achieve this bound, at the worst case,
asymptotically. Does the Poisson MLE achieve this bound for a finite sample size
(such as the one we have,n=365)?
I() = n E(
-_- n El
=
wemowpoissonMLE.si ,
iii) Va(I)
t.nl#Mt...xn))=nVanxi)=iUli)=
,
,
SOPoissonMLE-achievesthec-R10werbedcnlowerbandz.gl
n o.0 04504