1. what random variable is of interest here? what are the possible values for the random variable?

(Incomplete question); usually the sum of the probabilities for all values of a random variable is 1.

Step-by-step explanation:

A random variable is a numerical valued variable on a defined sample space of an experiment with expressions such as X or Y.

A good example is a company that wants to analyse the number of calls received at its Help Desk from 8 am to 12 pm in a month. The number of calls from customers at the Help Desk during the defined time period (8 am - 12 pm) is the random variable.

Another example is when a coin is tossed twice; the sample space is either {HH, HT, TH, TT} by assigning numerical values to the random variable we may define the random variable X as the total number of tails (T), meaning X values becomes 0,1 and 2 .