Machine Learning Probability Flashcards
Red Box / Blue Box
The red box has 2 apples and 6 oranges. The blue box has 3 apples and 1 orange.
Now suppose we pick a box at random, and it turns out to be a blue box. Then the probability of selecting an apple is just the fraction of apples in the blue box, is π(πΉ=π|π΅=π) =
π(πΉ=π|π΅=π) = 3/4
Red Box / Blue Box
The red box has 2 apples and 6 oranges. The blue box has 3 apples and 1 orange.
Now suppose we pick a box at random, and it turns out to be a red box. Then the probability of selecting an apple is just the fraction of apples in the red box, is π(πΉ=π|π΅=π)=
π(πΉ=π|π΅=π)= 1/4
Red Box / Blue Box
The red box has 2 apples and 6 oranges. The blue box has 3 apples and 1 orange.
Now suppose we pick a box at random, and it turns out to be a blue box. Then the probability of selecting an orange is just the fraction of oranges in the blue box, is π(πΉ=π|π΅=π)=
π(πΉ=π|π΅=π)= 1/4
Red Box / Blue Box
The red box has 2 apples and 6 oranges. The blue box has 3 apples and 1 orange.
Now suppose we pick a box at random, and it turns out to be a red box. Then the probability of selecting an orange is just the fraction of oranges in the red box, is π(πΉ=π|π΅=π)=
π(πΉ=π|π΅=π)= 3/4
Red Box / Blue Box
The red box has 2 apples and 6 oranges. The blue box has 3 apples and 1 orange.
A piece of fruit has been selected and it is an orange, the probability that the box is blue is
If the joint distribution of two variables factorizes into the product of the marginals, then X and Y are said to beβ¦
independent
π(π,π) = π(π)π π(π)
Marginal Probability
Conditional Probability
Joint Probability
Sum Rule
Product Rule
Symmetry
Using product rule
π(π,π) = π(π,π)
π(π,π) = π(π|π)π(π)
Using Sum and
Product rule
π(π) = Ξ£yπ(π,π) = Ξ£yπ(π,π) = Ξ£yπ(π|π)π(π)
Bayesβ Theorem
