# Posterior of Beta Distribution

Let $X$ be the number of packets that fail to reach their destination nodes from $n$ = 100 randomly selected packets. Use the Beta-binomial formulation to specify the posterior distribution $p(\theta|n,X)$, where $\theta$ (theta) is the probability of a packet failing to reach the destination node. Specify explicitly all the probability density functions of the model and state how the corresponding expected values are calculated.

This is what I got for now:

$p(\theta|n,X)= \frac{p(\theta,n,X)}{p(n,X)}$

Then

$p(\theta|n,X)= \frac{p(n|\theta,X)p(\theta,X)}{p(n,X)}$

And finally

$p(\theta|n,X)=\frac{p(n|\theta,X)p(X|\theta)p(\theta)}{p(X|n)p(n)}$

This doesn't make sense because $p(n)$ shouldn't have a value. Can someone tell me where to go or what am I doing wrong? I understand that the posterior should be a Beta Distribution.

• Hi, welcome to Cross Validated. When starting, it's a good idea to take the tour (as you alredy did) and to peruse the help pages. For example, you can increase the readability of your posts, and the likelihood of getting an answer, by writing formulas using Markdown sintax. This time I did it for you: can you check that the formulas have your intended meaning? – DeltaIV Feb 14 '17 at 15:49
• Also, "[..]routine question from a textbook, course, or test used for a class or self-study" need have the self-study tag, so I added it. – DeltaIV Feb 14 '17 at 15:50
• Hint: temporarily drop "$n$" from your notation (which you may do because it's fixed and you know its value). Now solve the problem. – whuber Feb 14 '17 at 15:59
• Hint #2: your formula cannot be resolved if you do not have a prior on $\theta$. – Xi'an Feb 14 '17 at 17:34
• @Xi'an this is the exact question text from the question and shouldn't the Beta distribution be on theta? – aQaddoumi Feb 14 '17 at 19:04