Expected number of random variables that must be observed

In summary, the conversation is about a mathematical equation and a potential typo in the answer given. The expert summarizes that the answer to (a) is correct, while the answer given for (b) is wrong due to a typographical error. The conversation ends with the expert thanking the other person for pointing out the error.
  • #1
WMDhamnekar
MHB
376
28
TL;DR Summary
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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  • #2
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.
 
  • #3
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.
 
  • #4
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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1. What is the expected number of random variables that must be observed?

The expected number of random variables that must be observed is the average number of random variables that would be observed if the experiment or process were repeated many times.

2. How is the expected number of random variables calculated?

The expected number of random variables is calculated by multiplying the probability of each possible outcome by the number of times that outcome would occur, and then summing these values.

3. Can the expected number of random variables be a decimal or fraction?

Yes, the expected number of random variables can be a decimal or fraction. It does not necessarily have to be a whole number.

4. What is the significance of the expected number of random variables in statistical analysis?

The expected number of random variables is an important concept in statistical analysis as it helps in predicting the outcome of an experiment or process. It also allows for the calculation of other statistical measures such as variance and standard deviation.

5. How does the expected number of random variables relate to the law of large numbers?

The law of large numbers states that as the number of trials or observations increases, the observed outcomes will approach the expected outcomes. Therefore, the expected number of random variables is a key component of the law of large numbers.

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