A little help understanding this bayesian problem (very basic)

[bennyska]

Homework Statement

so I'm trying to teach myself bayes, and i got a book, and I'm going through trying to do the exercises, and lo and behold, i get stuck on the first one. i thought i was getting it, but the answer given at the back of the book is different than mine.

Homework Equations

The Attempt at a Solution

i've attached three pictures. the first is the actual problem. so when i did it myself, i got that the first column of priors should all be 1/10, since we're assuming that the urn can contain 0 up to 9 red balls, for a total of 10 possibilities. the second picture is the answer, where it seems that i should have said 1/9 for the first column. the third picture is an example that seems to me to indicate that it should be 1/10. what am i missing?

 

[Simon Bridge]

There are 10 possible values for X, but there are only 9 balls to choose from.
What does the prior probability represent in this case?

 

[bennyska]

the prior probability represents the number of red balls in the urn. I'm told to assume that each possibility is equally likely. so there might be zero balls, 1 ball, 2 balls, etc, up to 9 balls. that should be a 1/10 probability for each case. furthermore, shouldn't the prior column sum up to 1? in the answer, doesn't the prior column sum up to 10/9?

 

[Ray Vickson]

the prior probability represents the number of red balls in the urn. I'm told to assume that each possibility is equally likely. so there might be zero balls, 1 ball, 2 balls, etc, up to 9 balls. that should be a 1/10 probability for each case. furthermore, shouldn't the prior column sum up to 1? in the answer, doesn't the prior column sum up to 10/9?

You are correct. Either the "zero balls" case should not be present (giving 1/9 probability of each of the others) or else it is present and all priors should be 1/10.

RGV

 

[bennyska]

thank you. also, i should have been more clear, the third picture was an example with the exact same problem, just fewer balls.

 

[Simon Bridge]

Yes - I'm inclined to agree that the text is mistaken in the model answer.
Frustrating, I know.

I had a go trying to identify the mistake but failed. Why would the author think to assume that P(X=x)=x/(N-1)?

I'd ignore the answers but do the analysis anyway. Pause at each step to see if what you get makes sense. The other one seems to be right - maybe you want to start with that instead.