=========================preview======================
(IELM313)Hw1[1].pdf
Back to IELM313 Login to download
======================================================
1.
2.
3.
4.
5.
6.
IELM313 Homework 1
Due 1 March 2006, before class starts
A production process manufactures alternators for outboard engines used in recreational boating. On the average, 1% of the alternators will not perform up to the required standards when tested at the engine assembly plant. When a large shipment of alternators is received at the plant, 100 are tested, and, if more than two are nonconforming, the shipment is returned to the alternator manufacturer. What is the probability of returning a shipment?
The time intervals between hits on a web page from remote computers are exponentially distributed, with a mean of 15 seconds. Find the probability that there is no hit within 30 seconds.
Three shafts are made and assembled into a linkage. The length of each shaft,
in centimeters, is distributed as follows:
Shaft 1: N(60, 0.09)
Shaft 2: N(40, 0.05)
Shaft 3: N(50,0.11)
(a)
What is the distribution of the length of the linkage?
(b)
What is the probability that the linkage will be longer than 150.2 centimeters?
(c)
The tolerance limits for the assembly are (149.83, 150.21). What proportion of assemblies are within the tolerance limits?
The arrival processes of regular customers and VIP to a sports facility can be modeled as Poisson processes with rates 20/hour and 5/hour, respectively. Suppose that the facility opens at 9am, and the fifth customer who is a VIP arrives at 9:10am. What is the probability that the next customer, either regular or VIP, arrives before 9:15am?
Develop a generation scheme for the triangular distribution with pdf
.1 (x .2),2 x 3
.
2
.
.1 x .
f ()=. ..2 . ,3 <x 6
x .2 . 3 .
.
.0, otherwise .
.
When a truck enters a terminal, it has a 90% chance to join the regular queue, which takes an exponential with mean 10 minutes to go through the terminal; it has a 10% chance to join a screening queue, which takes an exponential with mean 25 minutes to go through the terminal. How to generate random observations from the distribution that represents the time it takes for a truck to go through the terminal?