Final answer:
A continuous random variable is represented by a probability density function (pdf) and can take on any value within a certain range. The probability of a continuous random variable taking on a specific value is always zero.
Step-by-step explanation:
A continuous random variable is a variable that can take on any value within a certain range. It is represented by a probability density function (pdf), which is a graph that shows the probability of different values of the random variable.
The pdf is represented by the function f(x), and the area under the graph of f(x) represents the probability of the random variable falling within a certain range. The total area under the graph is always equal to one.
For example, if we have a continuous random variable X that can take on values between 0 and 10, the probability that X is equal to 7 (P(x = 7)) is equal to zero, because the probability of a continuous random variable taking on a specific value is always zero.