STAT230 Study Guide - Midterm Guide: Negative Binomial Distribution, Cumulative Distribution Function, Rush Hour

• School: University of Waterloo
• Department: Statistics
• Course: STAT230
• Professor: Changbao Wu

Document Summary

Let x be a random variable that takes possible values at non-negative integers and has cumulative distribution function. F (x) = p (x x) = 1 2 x for x = 0, 1, 2, (a) find the probability function of x. Soln: p (x = 5) = f (5) = 2 5; P (x 5) = 1 p (x 4) = 1 f (4) = 1 (1 2 4) = 2 4. Or: p (x 5) =(cid:80) x=5 2 x = 2 4. (c) find p (x = 5 | x 5) P (x = 5 | x 5) = [2] (a) find the probability p that there are 11 cars in a 30 second interval (30si). Soln: let x = #cars in a 30 second interval, then x poisson( ), with = 540/(60 2) = 4. 5. p = p (x = 11) =