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Piece-wise Continuous Probability Distributions

The probability distribution you just learned about sort of looks like a discrete probability distribution. But in fact, it is still a continuous distribution. It's called a piece-wise continuous distribution. If you're unfamiliar with piecewise functions, it just means that the function is divided into parts: check out this link for more examples.

How to Tell if this is Continuous or Discrete?

Ask yourself, is my variable of interest continuous or discrete? Hour, in this case, is a continuous variable because hour can be any decimal value between 0 and 24. So this is a continuous probability distribution.

You could rephrase this problem to make it discrete. If you counted how many people were born between 1am-2am, 2am-3am, 3am-4am, etc, the problem becomes discrete. You are slicing the hour variable so that it can only take on specific values ie 1, 2, 3, 4, 5, etc.