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

Question: 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

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.

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