# 代写math | mining代做 – math

### math代写 `````` math 170S Midterm 1 - Page 8 of 10 08/12/
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1. (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.
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#### lihclihoodfumtionuN.ie =

"

########

``````"
``````

#### i

=

``````365
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``````122 +^2 ^101 +^3 ^92
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### – 2

=

``````""
,
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##### 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)=
,
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``````SOPoissonMLE-achievesthec-R10werbedcnlowerbandz.gl

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