This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (b) Probability that more than 5 customers enter the bank during an hour. (c) Probability that exactly 1 arrival between 9:00am and 11:00am and exactly 2 arrivals between 10:00am and 12:00 noon. 5. A system consists of n components in parallel. The lifetimes of the components are i.i.d. exp ( λ ) random variables. The system functions as long as at least one of the n components is functioning. Let T be the lifetime of the system. Compute E [ T ]. 6. Let { N ( t ) ,t ≥ } be a PP ( λ ). Suppose a Bernoulli switching mechanism independently marks the events as either type 1 or type 2 with probability p and 1p , respectively. Let N i ( t ) be the number of type i events during (0 ,t ]. Let T i be the time until the ﬁrst event in the N i ( t ) process. Compute the joint distribution of ( T 1 ,T 2 ). 7. Let { N ( t ) ,t ≥ } be a PP ( λ ). Compute P £ N ( t ) = k  N ( t + s ) = k + m / for t ≥ 0, s ≥ 0, k ≥ 0, m ≥ . 1...
View
Full
Document
This note was uploaded on 05/03/2010 for the course AMS 342 taught by Professor Mitchell,j during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Mitchell,J

Click to edit the document details