ST102 Exercise XXXXXXXXXX–13) In this exercise you will practise deriving and working with sampling distributions of statistics. Q2 concerns, in particular, the use of the Central Limit Theorem to...

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Answered Same DayDec 22, 2021

Answer To: ST102 Exercise XXXXXXXXXX–13) In this exercise you will practise deriving and working with sampling...

Robert answered on Dec 22 2021
131 Votes
A1)
a) Since nXXX ...,, 21 is a random sample ,








n
i
X
tX
X
tMe
EtM
i
n
i
i
n
i
i 1
)(
)()()( 1
1
….By independendce.
Which gives us the Moment generating function of Poi (n )
b) 


n
i
i
n
X
XZ
1

Let Y=

n
i
iX
1

Thus Y takes the values 0,1,2…. With probabilities P(Y=y)=
!
)(
y
ne yn 

Thus Z takes the values 0,1/n,2/n….with probabilities P(Z=z)=
!
)(
z
ne zn 

C)...
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