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 + δ, where δ (a small positive number) is the “home field advantage.” There are no draws. Find:

(a) The PMF of N, the total number of games played. How does E[N] vary with δ?
(b) The probability that A wins the series, as a function of δ. If δ = 0.05, how much of an advantage does team A get from the series starting at their home field?

Let X ∼Geometric(0.8), and Y = min(X , 3).

(a) Determine the PMF of Y

(b) Calculate μY and σY . Compare these with μX and σX ; 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 λ = 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 μY = aμX + 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 μX and standard deviation σX , find the expected value, variance and standard deviation of the random variable Y , where: Y = X − μX σX

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 Essay Fount.

What Students Are Saying About Us

.......... Customer ID: 12*** | Rating: ⭐⭐⭐⭐⭐
"Honestly, I was afraid to send my paper to you, but you proved you are a trustworthy service. My essay was done in less than a day, and I received a brilliant piece. I didn’t even believe it was my essay at first 🙂 Great job, thank you!"

.......... Customer ID: 11***| Rating: ⭐⭐⭐⭐⭐
"This company is the best there is. They saved me so many times, I cannot even keep count. Now I recommend it to all my friends, and none of them have complained about it. The writers here are excellent."

"Order a custom Paper on Similar Assignment at! No Plagiarism! Enjoy 20% Discount!"