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You are given a discrete random variable distribution that has the 5 values {2, 3, 5, 9, k}. Sadly, the last value k or its probability P(k) are not known, but you do know that the population variance o2=13.75. Fiil in the missing value for the probability distribution: X 2 3 5 9 k P(x) 0.19 0.24 0.12 0.24 P(k) a) What is the value of P(k)? b) Write an expression involving k for the population mean u. c) Write an expression involving k for the sum {[x2.P(x)] d) Using the Alternate Formula for Population Variance or o2 x = [x2.P(x)] – u2x ) and the answers from parts (b) and (c) to write an equation involving k. e) Solve the equation above to discover the value of the missing variable value. Quadratic equation may be useful!