Problems that could occur in estimating n from a Binomial distribution

[lintmintskint]

Hi, I am doing the following question:

https://i.gyazo.com/f2e651334bcbd5f1dcb6d661e4160956.png

I have estimated both n and theta. But the part that is throwing me off is what problem could you encounter in estimating n here? My only idea is that it might be something to do with the sample size.

Any help? Thanks!

 

[mfb]

Think of how your estimate would look like for e.g. (5,7,6,5,4,6,7,6,10,7,7). Is that possible?

Another issue arises for small theta and large n.

 

[lintmintskint]

Think of how your estimate would look like for e.g. (5,7,6,5,4,6,7,6,10,7,7). Is that possible?

Another issue arises for small theta and large n.

Is the issue with the data set that you listed that n wouldn't be an integer? So we would have to round up or down to the nearest integer in some cases? Am I on the right track?

 

[mfb]

Well, it is an estimate, it doesn't have to be an integer. But that was not the problem I was thinking of.

 

[WWGD]

I don't know if this is an obvious/dumb question, but, when we consider the sample mean $\frac {1}{m}\Sigma_{i=1}^m x_i$ , do we consider $x_i$ as binary ( depending on the success criterion),

Think of how your estimate would look like for e.g. (5,7,6,5,4,6,7,6,10,7,7). Is that possible?

Another issue arises for small theta and large n.

I don't understand, aren't the sample values given in binary, i.e., as success failures? Or do we have to consider different criteria for this?

 

[mfb]

If we would be given the binary results of n trials, there would be no need to estimate n, we could simply count. As far as I understood the question, we get multiple samples of the binomial distribution, i. e. each number in my post is the number of successful attempts (out of an unknown n) in a series of attempts.