Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respectively, that 0,1,2 and 3 power failures will hit a certain subdivision in any given year. If X represents the no. of power failures hitting this subdivision given g(x) = 5x + 3, find E[g(x)).
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- (a) If the sum of the deviations of the numbers X1, X2, X3, ....., Xn from their mean, x, is zero. That is, E1(xi – x) = 0, show if k = x + c, that E-1(x; – k)? = E-1 (x; – x)2 + nc? Li%3D13. Suppose that X is a discrete random variable with probability mass function (pmf) as summarized in the table below. -3 f(x) 0.35 0.25 0.4 Find the cumulative distribution function (cdf) F(x) of X. You may either write F (x) as a piecewise defined function or sketch a graph of F(x). Also, no work is required to be shown in this problem.An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here
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