### Probability Distributions and Random Variables

Suppose I had two coins and I flipped both of them.  The possible combinations can be two heads, two tails, or one of each.  These combinations are all part of a sample space.

Now let's take this a step further.  Taking the above demonstration, we want to determine the probability that each combination would occur.

Assuming independence, we derive the following probabilities:

• • • All of these probabilities belong in a probability distribution.

### Deriving the Naive Bayes formula

In my previous post, I introduced a class of algorithms for solving classification problems.  I also mentioned that Naive Bayes is based off of Bayes' theorem.  In this post, I will derive Naive Bayes using Bayes' theorem.

### Deriving the Cost Function for Logistic Regression

In my previous post, you saw the derivative of the cost function for logistic regression as: I bet several of you were thinking, "How on Earth could you derive a cost function like this: Into a nice function like this: ?"

Well, this post is going to go through the math.  Even if you already know it, it's a good algebra and calculus problem. Read more