Final answer:
A random variable X should be defined by its context and can take on numerical values based on that context; non-numerical values like month names are not appropriate for this use. The distribution of X is key to calculating probabilities and statistical measures, and descriptive statistics such as mean and standard deviation make sense only when relevant frequencies or probabilities are associated with the values of X.
Step-by-step explanation:
When discussing a random variable X, it is first important to ascertain what the random variable represents. A random variable is typically a numerical value resulting from a random phenomenon. For instance, the random variable might represent the number of questions posted to a listserv on a given day, or it could be the length of time a certain process takes.
Once the random variable X is defined, the possible values that X may take on could be a whole number, a range of numbers, or a measurement, depending on the context. The distribution of X describes how probabilities are assigned to these possible values, and it is essential for calculating probabilities and other statistical measures.
If the random variable represents something like months of the year, values like 'Jan', 'Feb', ..., 'Dec' are not suitable because they are not numerical. Instead, assigning numerical values such as 1, 2, ..., 12 to represent January through December is appropriate. Descriptive statistics like mean and standard deviation could be meaningful if there's a frequency or probability associated with each month, otherwise, they would not make much sense.
Depending on the distribution and nature of the random variable, different statistics and descriptive measures might be recommended. If the distribution is normal, you might consider a confidence interval to estimate the population parameter in question.