(a) The number of trains.] that arrive at t he station in time t minutes is a Poisson random variable '~ h E [.J] = t. Find t such that P[.J > O] = 0.9. (b) The number of buses I< t hat arrive at t he station in one hour is a Poisson random variable with E [K] = 10. Find P [K = lO]. ( c) In a 1 ins interval, the number of hi ts Lon a \i\f eb server is a Poisson random variable 'vith expected value E[L] = 2 hits. What is P [L < 1]?

STAT-5615: Statistics in Research I Lecture 4 Probability & Probability Distributions Ott & Longnecker Chapter 4 Dr. Christian Lucero Virginia Tech Fall 2016 Introduction to Probability De▯nition A chance operation or random trial is a process or experiment that results in an outcome that cannot be predicted in advance with certainty. Example Tossing a coin, rolling a die, weighing a specimen, measuring the temperature of a patient or taking a while cell count are all examples of a chance operation. De▯nition The set of all possible outcomes of a chance operation is called a sample space for the chance operation. Example For a coin the sample space is the