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Here is my question:

You want to find proportion x of phones from a given company is defective. You are sent a box of 10 samples, and you find that two are defective.

  1. Compute the posterior distribution for x using a uniform prior distribution.

2.Some time later, you are sent a second batch of 10 phones from the same company, but a different model. You find that three examples are defective in this new batch. Compute the updated posterior distribution. (One the includes the estimate obtained from the first batch).

I am not sure how to calculate the exact value of the first question since I got a beta(3,8) on question1. Also, for question2, how can I use the posterior distribution(beta(3,8))in question 1 to update the new posterior question? (I am also not sure whether using binomial distribution or beta distribution for this question)Thanks.

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  • $\begingroup$ Why do you have a problem with question 1? Look at what it's asking from you. For question 2, think about what you want to use as a prior distribution to compute the posterior. Do you still want to use a uniform prior? Or do you want that prior to reflect knowledge you have gained in the past? $\endgroup$ – Bridgeburners May 8 '17 at 20:28
  • $\begingroup$ I want to use the knowledge gained from the first question, and for question1, is there any way to get a numerical value, apart from beta(3,8)? Thanks $\endgroup$ – user160608 May 8 '17 at 20:39
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If you read through What is the intuition behind beta distribution? you'll find an explanation. (Or actually, several explanations from various viewpoints. The question itself is broader than yours, but several answers give examples.)

Several answers use a baseball analogy, and in case you're not familiar with baseball, the idea is that you are "at bat" a certain number of times in a game and some number of those times at bat you succeed and manage to get a "hit". You thus have two numbers representing your "at bat performance" in a baseball game, which correspond to your example problem: "at bat" corresponds to your number of samples, "hit" corresponds to your number of defects.

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