Emails arrive in an inbox according to a Poisson process with rate (so the number of emails in a time interval of length t is distributed as Pois(t), and the numbers of emails arriving in disjoint time intervals are independent). Let X, Y, Z be the numbers of emails that arrive from 9 am to noon, noon to 6 pm, and 6 pm to midnight (respectively) on a certain day. (a) Find the joint PMF of X, Y, Z. (b) Find the conditional joint PMF of X, Y, Z given that X + Y + Z = 36. (c) Find the conditional PMF of X+Y given that X+Y +Z = 36, and find E(X+Y |X+ Y + Z = 36) and Var(X + Y |X + Y + Z = 36) (conditional expectation and conditional variance given an event are defined in the same way as expectation and variance, using the conditional distribution given the event in place of the unconditional distribution)

Stat 2000: Elementary Statistics Week One: Aug. 11th to 18th Defining Statistics Statistics consists of: ● Formulating a research question ● The collections of data ● Describing data ● Drawing conclusions or generalizations from data Statistics is the science of learning from data. The Statistical...