Probability Generating Functions

I understand part a of the question attached below, but am struggling in understand part b of the question. How would i go about solving the question? Any guidance would really be appreciated

Reply 1

ZHVelo

Not sure you attached anything.

Original post by ZHVelo

Not sure you attached anything.

just did, apologies for delay

Reply 4

ZHVelo

1. What does "each distributed as X" mean?
2. What have you been taught about the sum of independently 1. random variables?

Once you have this you can move on to the second part.

Reply 5

kparikh

Im still rather confused, i know that the sum of independent random variable are Gz(t) = Gx(t) * Gy(t), and that for Y = aX + b, Gy(t) = t^b(Gy(t^a)) but how do i use this to solve the question?
Thank You,

Reply 6

mqb2766

Original post by kparikh

Which distributions have you covered? If youve covered the negative binomial distribution, you should note that its mgf is the same as the product of n identical geometric distributions (sum of iid random variables, as per the question), so its the mgf of the geometric raised to the power n. The mean and variance are simply those of the negative binomial then. The question asks you to "write down" this stuff and its 5 marks in total, so its suggesting that very little working is required and you "must" have covered something like this?

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Probability Generating Functions

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