# 14+15 Flashcards

1
Q

What is a sample space, a sample point, joint distribution, and a probability model?

A

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.

2
Q

What is an event? How can we compute its probability on a joint distribution?

A

Any subset of points in a sample space. We can compute the probability of an event by summing the probabilities of the relevant points.

3
Q

How do we talk about continuous variables with regard to probability models?

A

Use the probability of a value being in a certain range. These are known as probability density functions.

4
Q

What is the gaussian function?

A

Normal distribution function, most continuous variables will hover around a central value, with less on the outskirts(bell curve).

5
Q

What is the mean and variance?

A

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.

6
Q

What is conditional probability?

A

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.

7
Q

Why is a full joint distribution so complex?

A

All variables have to be summed, meaning O(2^n) complexity for time and space.

8
Q

What is Bayes’ rule? What does it allow us to do?

A

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.

9
Q

How can we use conditional independence with Bayes’ rule?

A

If two conditions and conditionally independent, if we know what they are dependent on we can just multiply the probabilities together.