Please answer with and include R code

Exercise 4.3 (Modified) In Exercise 4.3, a nonhomogeneous Poisson process is defined to have the mean value function m(t) = {+2t, t >0. Use this process to answer the following questions. You might answer questions 2 - 5 theoretically or by simulation. 1. (2 points) Determine the intensity function (t) of the process. 2. (2 points) Find the probability to observe more than 10 events on the interval [4, 5]. 3. (2 points) Find the median of N(5) - N(4), i.e., find a I so that P{N(5) - N(4) 0. Use this process to answer the following questions. You might answer questions 2 - 5 theoretically or by simulation. 1. (2 points) Determine the intensity function (t) of the process. 2. (2 points) Find the probability to observe more than 10 events on the interval [4, 5]. 3. (2 points) Find the median of N(5) - N(4), i.e., find a I so that P{N(5) - N(4)