An engineer of a company wanted to obtain the information about the power failures in a small town. He recorded the number of power failures per day for the period of 102 consecutive days. He has found that there were 24 days with no failures, 30 days with 1 failure, 31 day with 2 failures, 11 days with 3 failures, and 6 days with 4 or more failures. The data obtained by the engineer are given in the table below. Number of power failures 0 1 2 3 4 or more per day Number of days with given number |24 30 31 11 6 of power failures per day Expected frequencies Test at the 0.05 level of significance whether the number of power failures in the town per day is a random variable having Poisson distribution with the value of parameter _ estimated from the sample data. Use R to answer questions a. - d. a. Show that estimated value of 1 is 1.46. b. Find the vector p of the values of Poisson probability mass function at the values of X = 0, 1, 2, 3, 4 or more. c. Check that all expected frequencies are no less than 5, and there is no need to combine the cells. d. Test the hypothesis using R that the number of power failures in the town per day is a random variable having Poisson distribution with the value of parameter 1 = 1.46. Use chi - square test. Assume 0.05 level of significance. Show the code, output, and make the conclusions based on obtained p -value