A statistics question need help.

ChrIsPuZa · 2016-05-03 06:15:46

Suppose a rv Y has mgf m(t)=e^[k(e^t -1)] / (1-bt)^a

a) obtain the mean and variance of Y (differentiate this mgt twice)

b)Suppose m(t) is the mgf of a rv W. Let r(t) be the natural logarithm of m(t),
i.e. r(t) = logm(t). Find r'(t) and r''(t) , and express r'(0) and r''(0)in terms of EW and VarW.

c) Use the result in (b) to find the mean and variance of the rv Y in (a)

d)Find the mean and variance of the rv Y in (a) using a method which does not involve any differentiation.

really difficult for me

bobbym · 2016-05-03 10:57:21

You can get the variance from the above.

b) There are missing characters.

ChrIsPuZa · 2016-05-04 02:28:20

Hi bobbym:

I'm also confused about (b) ,but I don't think there are missing characters. shall we consider about this :

r(t) = logm(t) , r'(t)=m'(t)/m(t) r''(t)=[m''(t) m(t)+(m'(t))^2] / (m(t))^2

and then we find r'(0)=m'(0) / m(0) =EW/m(0) .does this idea correct ? but how to use the EW and VarW to eliminate m(0)? thank you for your reply

bobbym · 2016-05-04 04:38:29

but I don't think there are missing characters

This is the way your post looks on my browser:

What the heck are those boxes for?

ChrIsPuZa · 2016-05-04 04:54:23

Hi:
sorry about that ,I don't know why there are some box appeared in your browser.

you can ignore these box ,the question is find the first and second derivative of r(t) and express the first and second derivative of r(0) in terms of E(W) and Var(W)

bobbym · 2016-05-04 05:24:25

r(t) = logm(t) , r'(t)=m'(t)/m(t) r''(t)=[m''(t) m(t)+(m'(t))^2] / (m(t))^2

I am getting

for the second derivative of r(t)

ChrIsPuZa · 2016-05-04 05:35:12

you are right, i make a mistake here . I have no idea about the second part question

'express the first and second derivative of r(0) in terms of E(W) and Var(W)'

bobbym · 2016-05-04 09:09:39

I am not getting that either, I am sorry.

ChrIsPuZa · 2016-05-04 16:19:19

thanks anyway

bobbym · 2016-05-04 16:33:23

Welcome to the forum. You might try the SE for the answer.

ChrIsPuZa · 2016-05-04 16:47:11

Hi bobbym:

do you have any idea about (d)? which method will not involve any differentiation to find mean and variance?

bobbym · 2016-05-04 16:57:55

I have been looking at that. Since the mean and variance are defined in terms of the derivatives of the MGF I do not know offhand how to get them without using differentiation.

Math Is Fun Forum

#1 2016-05-03 06:15:46

A statistics question need help.

#2 2016-05-03 10:57:21

Re: A statistics question need help.

#3 2016-05-04 02:28:20

Re: A statistics question need help.

#4 2016-05-04 04:38:29

Re: A statistics question need help.

#5 2016-05-04 04:54:23

Re: A statistics question need help.

#6 2016-05-04 05:24:25

Re: A statistics question need help.

#7 2016-05-04 05:35:12

Re: A statistics question need help.

#8 2016-05-04 09:09:39

Re: A statistics question need help.

#9 2016-05-04 16:19:19

Re: A statistics question need help.

#10 2016-05-04 16:33:23

Re: A statistics question need help.

#11 2016-05-04 16:47:11

Re: A statistics question need help.

#12 2016-05-04 16:57:55

Re: A statistics question need help.

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