University of California Characteristics of A Binomial Random Variable Questions Recall that the characteristics of a binomial random variable are:
1. The experiment consists of a fixed number (we usually use n) of trials.
2. The trials are independent.
3. There are only two possible outcomes on each trial, which for convenience we call success and failure.
4. The probability of a success (p), is the same for each observation.
5. If X is a binomial random variable then its mean is E[X]=?x=npE[X]=?x=np and its standard deviation is ?x=?np(1?p)?x=np(1-p) .
For the next three questions of the following examples, decide whether X is a binomial random variable using ONLY the information given. State why or why not.
Question 1: The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city, and asked whether he or she opposes the death penalty; X is the number who say Yes.
No, more than two outcomes.
Yes, meets all requirements of a binomial random variable
No, probability is not the same for each person.
No, trials are not independent.
Question 2: Suppose a jury of 12 people is chosen from the above pool, and this jury hears a case and discusses the verdict; X is the number who think the defendant is guilty.
Yes, meets all requirements of a binomial random variable.
No, there is not a fixed number of trials.
No, the trials are not independent.
No, there are more than two possible outcome
Question 4: Using the information from the previous question, find the expected number of people cured, i.e., E(X)E(X)(answer in decimal form round to nearest tenth if necessary).
Question 5: Now find the standard deviation of the number of people cured X (answer in decimal form round to nearest tenth if necessary).
Question 6: If 31 of the 40 people were cured, would this be unusual?
Also recall that the standard deviation of a Poisson is the square root of the mean: E(X)=?xE(X)=?x (also commonly written as ?? ) and SD(X)=?x=??SD(X)=?x=? .
Suppose a pet clinic gets an average of 9 cats per day to be spayed, and they only have the resources (material supplies and volunteer time) to spay a maximum of 14 cats on any given day. Can we find the probability that more cats will show up on a day than they can spay? We could work with the theoretical distribution, but instead, lets estimate it using relative frequencies in JMP. But FIRST let’s answer some theoretical questions:
Question 1: What are the theoretical expected value for the number of cats showing up at the clinic on a given day (don’t over think this)?
Question 2: What is the theoretical standard deviation for the number of cats showing up at the clinic on a given day? Round to two decimal places.
Why Choose Us
Top quality papers
We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.
Professional academic writers
We have hired a team of professional writers experienced in academic and business writing. Most of them are native speakers and PhD holders able to take care of any assignment you need help with.
If you feel that we missed something, send the order for a free revision. You will have 10 days to send the order for revision after you receive the final paper. You can either do it on your own after signing in to your personal account or by contacting our support.
All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.
Original & confidential
We use several checkers to make sure that all papers you receive are plagiarism-free. Our editors carefully go through all in-text citations. We also promise full confidentiality in all our services.
24/7 Customer Support
Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.
Try it now!
How it works?
Follow these simple steps to get your paper done
Place your order
Fill in the order form and provide all details of your assignment.
Proceed with the payment
Choose the payment system that suits you most.
Receive the final file
Once your paper is ready, we will email it to you.
No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.
You are welcome to choose your academic level and the type of your paper. Our academic experts will gladly help you with essays, case studies, research papers and other assignments.
Admission help & business writing
You can be positive that we will be here 24/7 to help you get accepted to the Master’s program at the TOP-universities or help you get a well-paid position.
Editing your paper
Our academic writers and editors will help you submit a well-structured and organized paper just on time. We will ensure that your final paper is of the highest quality and absolutely free of mistakes.
Revising your paper
Our academic writers and editors will help you with unlimited number of revisions in case you need any customization of your academic papers