Summary
Summary OPMT1130 ALL NOTES + Midterm/Final
- Course
- Institution
OPMT1130 ALL NOTES + Midterm/Final
[Show more]
Seller
Follow
ungieratoskar
Content preview
OPMT 1197Business Statistics
Lecture 11/12: Exponential and Uniform Distributions
Exponential Probability Distribution
Examples where it applies:
The length of time between telephone calls or between arrivals at a service station
The time required to load a truck
1. Used for continuous variables only since time is continuous.
2. Right skewed (mean > median) since the majority of the values (i.e. the waiting times) tend
to be on the left-side, or lower end, of the distribution.
3. The values can never be negative since waiting time cannot be negative.
It is often used to model the distribution of lifetimes for components, batteries and light bulbs.
It is used because of the “memoryless” property of the exponential distribution. If a component
has lasted 300 hours then the probability that it will last another 300 hours is the same as the
original distribution of lifetime. At each point the component has no effect of wear. The
component forgets that it already lasted 300 hours and starts fresh.
x
Cumulative Probability: PX x 1 e x and P X x e
• X = amount of time between arrivals • μ = the average time between arrivals (occurrences)
• Standard Deviation = Mean μ
1. The time it takes to load a truck at Schips loading dock averages 15 minutes. If the time it
takes to load a truck follows an exponential distribution, find the probability that it takes:
(a) 6 minutes or less to load a truck? (b) longer than 18 minutes to load a truck?
(c) between 6 and 18 minutes to load a truck? (d) Calculate the standard deviation.
The exponential distribution is closely related to the Poisson distribution. For example, the
Poisson distribution counts the number of customers that arrive at a bank during an hour while
the exponential distribution looks at the length of time between customers or the length of
time until the next customer arrives.
Poisson: Number of events over a time interval Exponential: Length of time between events
2. On Monday mornings, at a CIBC branch, an average of 12 customers arrive every hour.
The time between arrivals follows an exponential distribution.
(a) The average time between customers is?
(b) What is the probability that the next customer will arrive within the next 3 minutes?
(c) Given that no customers arrived on Monday morning between 10:15 and 10:25 am, what
is the probability that the next customer will arrive by 10:30 am?
Sol: 1. (a) 0.3297 (b) 0.3012 (c) 0.3691 (d) 15 minutes 2. (a) 5 minutes (b) 0.4512 (c) 0.6321
1 of 3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ungieratoskar. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now