## Description

I don't know how to solve this question. Thank you so much.

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## Explanation & Answer

Hi, Attached is the details for a-c, d) I am not sure how to do it now, I will look up to find some hints, thank youJames,

a)

(tY ) n

)

n!

n 0

m(t ) E (etY ) E (

dm

E (Y )

dt t 0

d 2m

E (Y 2 )

2

dt t 0

ln m(t ) k (et 1) a ln( 1 bt )

1 dm

ab

ket

m(t ) dt

1 bt

dm

ab

m(t )( ket

)

dt

1 bt

dm

m(0)( k ab)

dt t 0

E (Y )

(k ab)

d 2 m dm(t )

ab

ab 2

t

t

(ke

) m(t )( ke

)

dt

1 bt

dt 2

(1 bt ) 2

d 2m

(k ab) 2 (k ab 2 )

dt 2 t 0

E (Y 2 )

Var (Y ) E (Y 2 ) ( E (Y )) 2 (k ab) 2 (k ab 2 ) (k ab) 2

(k ab 2 )

b)

E (W )

dm

dt 0

d 2m

dm 2

Var (W ) 2 (

)

dt 0

dt 0

m(0) 1

r ' (t )

1 dm

m(t ) dt

r ' ' (...