What is a sample space, a sample point, joint distribution, and a probability model?
A model of all possible ways the world can be. Each possible combination is a sample point. A probability model assigns a probability to each sample point in a sample space(probability distribution).
A joint distribution is a probability distribution over two or more random variables.
What is an event? How can we compute its probability on a joint distribution?
Any subset of points in a sample space. We can compute the probability of an event by summing the probabilities of the relevant points.
How do we talk about continuous variables with regard to probability models?
Use the probability of a value being in a certain range. These are known as probability density functions.
What is the gaussian function?
Normal distribution function, most continuous variables will hover around a central value, with less on the outskirts(bell curve).
What is the mean and variance?
The mean is the expected value of the random variable itself. The variance is the expected value of the squared deviation of the random variable from its mean.
What is conditional probability?
Conditional probability is the probability of an event given information about another event. This is represented as P(a|b) meaning probability of a given b. It is equal to P(a and b)/P(b) is P(b) isn’t 0.
Why is a full joint distribution so complex?
All variables have to be summed, meaning O(2^n) complexity for time and space.
What is Bayes’ rule? What does it allow us to do?
P(b|a) = (P(a|b)P(b))/P(a). This allows us to calculate the probability of an effect given a cause instead of the other way around.
How can we use conditional independence with Bayes’ rule?
If two conditions and conditionally independent, if we know what they are dependent on we can just multiply the probabilities together.