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:

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.

Question	Answer
Probability of continuous random variable X taking value between a and b	P(a \leq X \leq b) = \int_a^b f(x)\,dx
What is f(x) in the formula P(a \leq X \leq b) = \int_a^b f(x)\,dx?	f(x) is the probability density function of the continuous random variable X.
How do you find the probability that a continuous random variable X lies between a and b?	Evaluate the integral \int_a^b f(x)\,dx, where f(x) is the probability density function of X.