Please answer step by step. thank you. Explain all details and write the coding part. All parts is from same.question so all of them need to be answered. Write down all coding part. thanks

Emails arrive at an Inbox according to a Poisson process at a rate of 20 per hour. Each email is spam with chance 1/100 independently of all others. Emails that are not spam are called "ham". Suppose I start watching the process at time 0. Define the following random variables: . M 30 is the number of emails that arrive in the first half-hour that I watch. . For a positive integer k let I'M , be the arrival time of the kth email. a) What is the distribution of M 30? b) Fill in the blanks. The first blank should be filled in with one of the comparison operators >, , 30 minutes Use this and Part a** to write P(TMS > 30 minutes) as a finite sum, and then use the code cell below to write an expression that evaluates to the numerical value of the probability. **Use only discrete distributions in the calculation. K # 4b c) Find the chance that in a fixed five-hour interval, there are at least 80 ham emails and at most one spam email. Then use the code cell below to write an expression that evaluates to the numerical value of this probability. 1 : H # 4c . . d) Suppose I watch the process for two hours. Given that there were 35 ham emails in that entire period, what is the conditional distribution of the number of ham emails in the first of the two hours? e) Suppose I watch the process for two hours. Given that there were 35 ham emails in that entire period, what is the conditional distribution of the number of spam emails in the first of the two hours