Probability Showing Point of Similarity in Random Variables
Define each of the following terms and provide an example for each: an event, union of events, intersection of events, sample space, mutually exclusive events, the complement of an event, containment, the null event, disjoint events, the probability of an event, probability space, probability by counting, probability of union of events, probability of union of disjoint events, the relation between probabilities of complementary events, relation between the probabilities of the contained event and the probability of its container, conditional probability and its constitutive relation, contingency tables, independent events.
. 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?
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● 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 union of disjoint events exhibit itself when dealing with a (discrete or continuous) random variable? Provide an example.