distribution of a continuous variable

As you remember, we grouped the values of a continuous variable in intervals.

A probability density function, f, is a function that positively verifies that f(x)≥0 is always accomplished and the area between X-axis and the graph of the function is 1.

Example:

Then, the probability of an interval is the area under f in the interval. In the example: P(1≤x≤2)=1/3

The distribution function of a continuous variable is F(x_i)=P(x≤x_i). In the example: F(2)=P(x≤2)=2/3