The exponential random variable arises in the modeling of the time between occurrence of events. An engineer is building a model to observe the distribution of the lifetime T for an electronic component. Suppose that the time T (in year) belongs an exponential distribution f(x)-?e-1x11(x)) , with an expected value of t years. Formulate and explain the mathematical steps to derive the random numbers of the uniformly distributed random numbers at interval [0,1]. Fort 3,4,5, please report the followings: Formulate and explain the mathematical steps of the inverse transformation method Develop a script that implements the steps. print out 100 such random numbers of exponential distribution in a table with Matlab Mark these random numbers on the x-axis of the PDF plot with Matlab Elaborate the results that you have generated in b and c (for example the location of the random numbers). a. b. c. d. Please note that you must generate uniformly distributed random numbers first, and 'transform' them into random numbers of the exponential distribution. The exponential random variable arises in the modeling of the time between occurrence of events. An engineer is building a model to observe the distribution of the lifetime T for an electronic component. Suppose that the time T (in year) belongs an exponential distribution f(x)-?e-1x11(x)) , with an expected value of t years. Formulate and explain the mathematical steps to derive the random numbers of the uniformly distributed random numbers at interval [0,1]. Fort 3,4,5, please report the followings: Formulate and explain the mathematical steps of the inverse transformation method Develop a script that implements the steps. print out 100 such random numbers of exponential distribution in a table with Matlab Mark these random numbers on the x-axis of the PDF plot with Matlab Elaborate the results that you have generated in b and c (for example the location of the random numbers). a. b. c. d. Please note that you must generate uniformly distributed random numbers first, and 'transform' them into random numbers of the exponential distribution