Final answer:
A continuous random variable takes uncountable values obtained by measuring. It is described by a probability density function (PDF) and cumulative distribution function (CDF). In contrast, a discrete random variable takes countable values and is described by a probability mass function (PMF) and cumulative distribution function (CDF).
Step-by-step explanation:
A continuous random variable is a random variable that takes uncountable numbers of values, such as time or weight. The values of a continuous random variable are obtained by measuring rather than counting. For example, the temperature of a randomly selected day in June or the height of a randomly selected high school student.
The probability density function (PDF) is used to describe probabilities for continuous random variables. It gives the probability density at each point on the curve. The cumulative distribution function (CDF) gives the probability that the variable falls below a certain value.
In contrast, a discrete random variable takes countable values and is described by a probability mass function (PMF), which gives the probability of each value. The cumulative distribution function (CDF) gives the probability that the variable falls below or equals a certain value.