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#### marcadams267

##### New member

- Aug 26, 2019

- 8

Suppose that Carl wants to estimate the proportion of books that he likes, denoted by π. He modeled

π as a probability distribution given in the following table. In the year 2019, he likes 17 books out of a

total of 20 books that he read. Using this information, determine πΜ using Maximum a Posteriori method.

_____________

π | 0.8 | 0.9 |

π(π )| 0.6 |0.4 |

_____________

My attempt at a solution:

I know I have to use Bayes theorem to solve this, so the equation is:

f(π |x) = (f(π )f(x|π ))/f(x).

So next, I have to find f(π ) and f(x|π ) and realize that f(x) is the marginal pdf of x - which I can solve by

integrating f(π )f(x|π )dπ

However, I'm stuck on the first step as I'm not entirely sure how to express the data on the table as the pdf f(π ) and the conditional probability f(x|π ).

While I can reasonably attempt the math, I would like help translating the words of this problem into actual equations that I can use to solve the problem. Thank you