Probability density function
A probability density function (PDF) describes a continuous random variable: probability is the area under its curve between two values, not the height at a single point.
See it move
A vending machine's refill time is spread evenly between 20 and 40 minutes, so its density is 1/20 across that range. The probability of a refill taking between 25 and 30 minutes is the area of that stretch: a width of 5 minutes times a height of 1/20, giving 5/20, or 25%.
The formula
Variables
- Lower bound of the interval
- Upper bound of the interval
- Value of the probability density function at x
Gives the probability that a continuous random variable falls between two values, as the area under its density curve over that interval.
Check yourself
A vending machine's refill time is uniformly distributed between 0 and 10 minutes, so its probability density function is f(x) = 0.1 for 0 ≤ x ≤ 10 and 0 elsewhere. What is the probability that the refill time is between 3 and 7 minutes?