Answer to Question 1
First, the random variable of interest must be discrete. Then look to see whether there are a specified number of trials, of which there are only 2 possible outcomes, each of which is conducted in an identical manner. Then determine whether it is possible to count the number of successes and the number of failures that occur when the trials are performed. Finally, check to see if the probability of a success can be assumed to remain constant from trial to trial.
Answer to Question 2
The expected value is the weighted average of the possible values for the discrete random variable where the weights are the individual probabilities associated with each possible value. The expected value represents the long-run average value for the random variable if the experiment that generates the random variable is repeated a very large number of times.
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