Continuous random probability

Continuous random probability

The probability of a continuous random variable taking on a value between a and b can be found using:

P(a \leq X \leq b) = \int_a^b f(x)\,dx

Where:

• X is the continuous random variable.
• f(x) is the probability density function of X.
• a and b are the bounds of the interval we’re interested in.

Solving that integral between any two values for a and b will give us the probability of a continuous random variable (following that probability density function) taking on a value between a and b.