Brilliant - Predictions and Probability Flashcards
What is the assumption we make when dealing with predictions?
That the future will behave like the past.
What does the number of times an outcome appears in our data set directly relate to?
It directly relates to how likely it is to happen again in the future.
What is a probability?
The number of times an event appears in a dataset divided by the total number of records.
What is a Probability Mass Function (PMF)?
It lists the probabilities for all events.
What is normalization?
When you rescale a bar chart by the total height.
How do we handle any new information?
We ignore data that doesn’t match the conditions.
What does the joint probability P9A and B) measure?
It measures the chance the two events A and B will happen together.
How are joint and conditional probabilities connected?
They are connected through P(A and B) = P(A|B) * P(B)
What is the Law of Total Probability?
If the data splits with no overlap between B₁ and B₂, we have: P(A|B₁) * P(B₁) + P(A|B₂) * P(B₂).
What does the Law of Total Probability allow us to do?
It lets us update our probabilities when filtering isn’t an option.
What is Bayes’ Rule?
P(A|B) = P(B|A) * [P(A)] / [P(B)]
What does Bayes’ Rule allow us to do?
It allows us to update probabilities in light of new evidence.
What is the Cumulative Distribution Function (CDF)?
P(X ≤ x); the CDF accumulates the PMF values–if X is a random quantity, P(X ≤ x) is the sum of all the PMF values up to and including the one for x.
What happens to the CDF if x becomes negative?
Then CDF(x) drops to 0.
What happens to the CDF when x is big enough?
Then CDF(x) is the sum of all the PMF values, so it has to be 100%.
