- Two teams A and B play a best-of-three games series; the series ends as soon as one team has won twice. The series starts at Aâ€s home field, then goes to Bâ€s, and then returns to Aâ€s (if a third game is played.) Assume that the team playing at home has a probability of winning
p = 0.5 + Î´, where Î´ (a small positive number) is the â€œhome field advantage.â€ There are no draws. Find:
- (a) The PMF of N, the total number of games played. How does E[N] vary with Î´?
- (b) The probability that A wins the series, as a function of Î´. If Î´ = 0.05, how much of an advantage does team A get from the series starting at their home field?
- Let X âˆ¼Geometric(0.8), and Y = min(X , 3).
- (a) Determine the PMF of Y
- (b) Calculate Î¼Y and ÏƒY . Compare these with Î¼X and ÏƒX ; how and why do they differ?
- Buses arrive at the station randomly and independently, at a rate of 1 per five minutes; the number that arrive in t minutes is thus a Poisson random variable B with Î» = 0.2t.
- (a) Calculate the probability that exactly two buses come in a 10 minute interval.
- (b) How much time should you allow so that there is a 0.99 probability that at least one bus will arrive?
- (c) Suppose that, over a 10 minute interval, one bus arrives during the first x minutes and a second bus arrives during the remaining time. Calculate the probability of this event as a function of x; x does not have to be a whole number. Compare your result with the answer to (a); how and why do the differ?
- A general linear transformation Y = aX + b scales the PMF of X by a factor a and shifts it such that Î¼Y = aÎ¼X + b. Demonstrate this by calculating the PMF of Y when X is Bernoulli(1/2). Plot both PX (x) and PY (y), including the means on your plots.
- If X is a random variable with mean Î¼X and standard deviation ÏƒX , find the expected value, variance and standard deviation of the random variable Y , where: Y = X âˆ’ Î¼X ÏƒX
WE WRITE ESSAYS FOR STUDENTS
Tell us about your assignment and we will find the best writer for your projectWrite My Essay For Me
Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount!
Use Discount Code “Newclient” for a 15% Discount!
NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you.
The post probability-theory-and-statistics-5 appeared first on Quality Nursing Writers.
probability-theory-and-statistics-5 was first posted on February 23, 2021 at 11:05 pm.
©2019 "Essay Lords | Bringing Excellence to students world wide". Use of this feed is for personal non-commercial use only. If you are not reading this article in your feed reader, then the site is guilty of copyright infringement. Please contact me at email@example.com
Are you facing the challenge of a looming assignment deadline? We have got a straightforward solution just for you! Just fill out our order form, detailing your specific instructions. Be confident knowing that our team is composed of expert writers who excel in their respective fields of study. They make use of extensive databases, high-quality online libraries, and the latest periodicals and journals to ensure the delivery of papers that are of the highest quality, customized to meet your needs. Rest assured that thorough research is conducted for every essay, and our unparalleled expertise spans a variety of topics. Additionally, our diverse team of writers covers a wide array of disciplines. You can trust that all our papers are crafted from the ground up, ensuring originality and uniqueness.
Write my essay. We write papers from scratch and within your preferred deadline.