- #1
marcadams267
- 21
- 1
Here's the problem:
Suppose that Carl wants to estimate the proportion of books that he likes, denoted by ๐. He modeled
๐ 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 ๐ฬ using Maximum a Posteriori method.
_____________
๐ | 0.8 | 0.9 |
๐(๐ )| 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(๐ |x) = (f(๐ )f(x|๐ ))/f(x).
So next, I have to find f(๐ ) and f(x|๐ ) and realize that f(x) is the marginal pdf of x - which I can solve by
integrating f(๐ )f(x|๐ )d๐
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(๐ ) and the conditional probability f(x|๐ ).
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
Suppose that Carl wants to estimate the proportion of books that he likes, denoted by ๐. He modeled
๐ 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 ๐ฬ using Maximum a Posteriori method.
_____________
๐ | 0.8 | 0.9 |
๐(๐ )| 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(๐ |x) = (f(๐ )f(x|๐ ))/f(x).
So next, I have to find f(๐ ) and f(x|๐ ) and realize that f(x) is the marginal pdf of x - which I can solve by
integrating f(๐ )f(x|๐ )d๐
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(๐ ) and the conditional probability f(x|๐ ).
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