Let X be a discrete random variable with a finite number of possible values, say, x1, x2, . . . , xm. For convenience, set pk = P(X = xk ), for k = 1, 2, . . . ,m. Think of a horizontal axis as a seesaw and each pk as a mass placed at point xk on the seesaw. The center of gravity of these masses is defined to be the point c on the horizontal axis at which a fulcrum could be placed to balance the seesaw.
Relative to the center of gravity, the torque acting on the seesaw by the mass pk is proportional to the product of that mass with the signed distance of the point xk from c, that is, to (xk − c) · pk. Show that the center of gravity equals the mean of the random variable X.
Answer to relevant QuestionsGive two examples of Bernoulli’s trails other than those presented in the text. n = 5, p = 0.6, P(X = 3) a. The binomial probability formula, Formula 5.4 Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a). A student takes a multiple-choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60% or better. Suppose that the student was unable to find time to study for the exam and just ...Sickle cell anemia is an inherited blood disease that occurs primarily in blacks. In the United States, about 15 of every 10,000 black children have sickle cell anemia. The red blood cells of an affected person are abnormal; ...The population of Seoul was studied in an article by B. Lee and J. McDonald, "Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women" (Urban Studies, Vol. 40, ...
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