During the first round of enrollment, students begin registering for classes at the top of each hour.There's a mad rush at the beginning of the hour, and then logins taper off. Let X(t) = the numberof logins t minutes into the hour, and suppose X(t) can be modeled by a nonhomogeneous Poissonprocess with intensity function 1(t) = 500/(t + 1)² for 0 < t < 60.(a) What is the expected number of students that will log into the registration system in the first5 min of the hour? In the last 5 min of the hour?(b) What is the probability that no students log in during the last 5 min of an hour?(c) The registration system will crash if more than 450 students log in during any 5-min period.What is the probability that this occurs in the first 5 min of an hour? (You will need to usesoftware or a Central Limit Theorem approximation to determine this probability.)

We are provided with the following information Xt=number of logins t minutes into the hour, where…

During the first round of enrollment, students begin registering for classes at the top of each hour. There’s a mad rush at the beginning of the hour, and then logins taper off. Let X(t) = the number of logins t minutes into the hour, and suppose X(t) can be modeled by a nonhomogeneous Poisson process with intensity function 2(t) = 500/(t + 1)² for 0 < t < 60. (a) What is the expected number of students that will log into the registration system in the first %3D 5 min of the hour? In the last 5 min of the hour? (b) What is the probability that no students log in during the last 5 min of an hour? (c) The registration system will crash if more than 450 students log in during any 5-min period. What is the probability that this occurs in the first 5 min of an hour? (You will need to use software or a Central Limit Theorem approximation to determine this probability.)