I Expected number of random variables that must be observed

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The expected number of random variables to be observed is calculated as E[N] = p^{-4}q^{-3} + p^{-2}q^{-1} + 2p^{-1}. There was a discussion about a potential typographical error in the expression for XN, which should be corrected to XN = p^{-4}q^{-3} - p^{-3}q^{-2} - p^{-2}q^{-1} - p^{-1}. The author’s answer to part (a) was confirmed as correct, while another participant acknowledged their mistake. The method used in the calculations was praised as innovative and effective. Overall, the conversation focused on clarifying the correct formulas and acknowledging errors in the initial responses.
WMDhamnekar
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Expected number of random variables that must be observed before any specific sequence.
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In my opinion, answer to (a) is ## \mathbb{E} [N] = p^{-4}q^{-3} + p^{-2}q^{-1} + 2p^{-1} ##
In answer to (b), XN is wrong. It should be XN=p-4q-3 - p-3 q-2- p-2 q-1 - p-1. This might be a typographical error.
Is my answer to (a) correct?
 
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WMDhamnekar said:
In my opinion, answer to (a) is ## \mathbb{E} [N] = p^{-4}q^{-3} + p^{-2}q^{-1} + 2p^{-1} ##
Please explain your reasoning.

For b) I agree with you.
 
haruspex said:
Please explain your reasoning.

For b) I agree with you.
Answer to (a) given by author is correct. My answer is wrong. Thanks for bringing my error to my notice.
 
WMDhamnekar said:
Answer to (a) given by author is correct. My answer is wrong. Thanks for bringing my error to my notice.
You are welcome.
I had never seen this method before. It's brilliant- thanks for posting.
 
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