• What makes a function of a discrete variable a candidate for a discrete random variable distribution? What about the counterpart of this candidacy in the case of a continuous variable?
• Explain the significance of the mean, variance, and standard deviation for a random variable. Does the significance change when passing from the discrete case to the continuous case?
• Provide a detailed discussion on the distribution of a discrete random variable, in general terms, and then provide a numerical example of this distribution. What are the mean and the standard deviation in your example? How does this differ in the case where the random variable is continuous? Explain.
• How does the probability of the union of disjoint events exhibit itself when dealing with a (discrete or continuous) random variable? Provide an example.