Exam 3 in STA 4321/5325 - Spring 2005 - Prof. Lawrence Herman Winner, Exams of Probability and Statistics

Download Exam 3 in STA 4321/5325 - Spring 2005 - Prof. Lawrence Herman Winner and more Exams Probability and Statistics in PDF only on Docsity! STA 4321/5325 Exam 3 – Spring 2005 PRINT Name________ Show all work! 1. Truck arrivals at a company loading dock follow a Poisson distribution with parameter . The dock foreman selects at random n days and checks the records to determine how many trucks arrived each day. Derive the distribution of the sum of the arrivals for the n day, assuming the numbers are independent of one another, by completing the following parts. a) State the moment generating function for Xi b) Obtain the moment-generating function for U=X1+…+Xn (show all work and state any results you use in intermediate steps) c) Based on your result from b), what is the distribution of U (state any pertinent parameters). 2. X1,…,X25 are independent and normally distributed with mean 75 and standard deviation = 20. State the probability distribution of the sample mean: 25 25 1   i iX X 3. Let X1 and X2 represent the proportions of time, out of one workweek that employees I and II spend on their assigned tasks. The joint relative frequency behavior of X1 and X2 is modelled by the probability density function:      elsewhere0 10,10 ),( 212121 xxxx xxf a) Give the marginal distribution for X1 and sketch it. b) Set up the integral (be very specific on limits of integration) to find P(X1+X2 < 1)