Final answer:
A continuous random variable can take on an infinite number of values in an interval and is measured rather than counted. Continuous variables are used in various fields such as reliability, and they are essential in advanced statistical models like the GLM with a log-link. The distinction between continuous and discrete variables is primarily in how they are defined and whether they are measured or counted.
Step-by-step explanation:
A continuous random variable is one whose outcomes are measured and can take on an infinite number of different values within an interval. Examples of continuous random variables include baseball batting averages, IQ scores, the length of time a long-distance telephone call lasts, the amount of money a person carries, the length of time a computer chip lasts, and SAT scores. The field of reliability, among others, depends heavily on such variables.
In contrast, a discrete variable is one that has countable outcomes. Examples of discrete variables include the number of books purchased and the number of books sold. Continuous variables are represented with outcomes like the amount of money spent on books and the amount of money received when selling them.
The GLM (Generalized Linear Model) with a log-link is particularly useful for modelling responses that are continuous random variables, ensuring predicted values are positive, which is logical for many types of data such as counts and rates.
It is important to understand how the variable is defined to determine whether it is continuous or discrete. For example, if you measure the exact distance you drive to work, that distance would be a continuous variable, whereas if you're counting the number of miles rounded to the nearest mile, it becomes a discrete variable.
The complete question is: continuous variables when a log-link is used (GLM) is: