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Branching processes (probability)

I'm getting confused by this question:

Consider a branching process which starts with one individual in generation 0. The number of offspring X for an individual has the same distribution for all individuals in all generations and E(X) = μ. Let Yn be the number of individuals in generation n.

If the process started with k individuals instead of one individual, what is E(Yn)?
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Smaug123
15
Original post by shawn_o1
I'm getting confused by this question:

I'd be very surprised if the answer weren't just kk times "the expectation if we started only with one individual", because the k processes we're running are independent. Do you know how to do the expectation with only one individual?
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shawn_o1
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21
Original post by Smaug123
I'd be very surprised if the answer weren't just kk times "the expectation if we started only with one individual", because the k processes we're running are independent. Do you know how to do the expectation with only one individual?


Yes, E (Yn) = (E(X))^n

I'm confused because the last time I checked, every branching process Yn has Y0 = 1?
Reply 3
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Smaug123
15
Original post by shawn_o1
Yes, E (Yn) = (E(X))^n

I'm confused because the last time I checked, every branching process Yn has Y0 = 1?

Imagine instead that you're running k independent branching processes.

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