# Discerning The Set Of Values For A Random Variable

The question is:

For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete.

a. $X=$the number of unbroken eggs in a randomly chosen standard egg carton

b. $Y=$ the number of students on a class list for a particular course who are absent on the first day of classes

c.$U=$ the number of times a duffer has to swing at a golf ball before hitting it

d. $X=$ the length of a randomly selected rattlesnake

e. $Z=$ the amount of royalties earned from the sale of a first edition of 10,000 textbooks

f.$Y=$ the pH of a randomly chosen soil sample

g. $X=$ the tension (psi) at which a randomly selected tennis racket has been strung

h. $X=$ the total number of coin tosses required for three individuals to obtain a match (HHH or TTT)

For some odd reason, the answer key doesn't provide answers to every part.

For parts d) f), and g), I know that the random variable is continuous, but how would I represent the set of possible values in set builder notation? I could write it only in intervalic notation.

For parts b), c), and h), the random variables are discrete, but would it be countably infinite?

As for part e), the answer key says that it is discrete, but I feel it could be continuous. What if each textbook was valued at $50 \pi$?

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Let's take d) as an example. The length $X>0$ for sure, but that's all you know. You could imagine a snake of arbitrarily large length, although the longer it is, the more remote a chance you'd ever find one. That of course would be reflected in the probability distribution. So I would say that $0 < X < \infty$. Reason the others the same way as well (although I seem to remember a pH having a max value of $14$).