# 4.4 Probability Distributions for Continuous Random Variables

The graphical form of the probability distribution for a continuous random variable `x` is a smooth curve that might appear as shown in Figure 4.13. This curve, a function of `x`, is denoted by the symbol *f(x)* and is variously called a probability density function**,** a frequency function**,** or a probability distribution**.**

The areas under a probability distribution correspond to probabilities for `x`. For example, the area `A` beneath the curve between the two points `a` and `b`, as shown in Figure 4.13, is the probability that `x` assumes a value between `a` and $b(a<x<b).$ Because there is no area over a single point, say, $x=a$, it follows that (according to our model) the probability associated with ...

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