An individuals work inbox receives emails throughout the day, and the number of emails arriving follows a Poisson distribution with an average of 6 emails per hour.

(a) Calculate the probability of receiving at least 4 emails in the next 20 minutes

.(b) Find the probability of exactly 10 emails arriving in the next 2 hours.

(c) Calculate the expected number of emails the individual will receive in the next90 minutes.3

(d) Determine the probability of receiving more emails in the next 45 minutes thanin the previous 30 minutes.

(e) Given that the individual has already received 8 emails in the first hour, findthe probability of receiving 2 or fewer emails in the second hour.(f) Calculate the probability of not receiving any emails in the next 30 minutes,given that no emails arrived in the previous 45 minutes.