Publications by Amber Ferger
DATA 605 - Assignment 8
Problem 11 (pg.363) The price of one share of stock in the Pilsdoff Beer Company (see Exercise 8.2.12) is given by \(Y_n\) on the \(n\)th day of the year. Finn observes that the differences \(X_n = Y_{n+1} −Y_n\) appear to be independent random variables with a common distribution having mean \(\mu = 0\) and variance \(\sigma^2 = \frac{1}{4}\)....
3967 sym R (422 sym/7 pcs)
DATA 605 - Week 9 Discussion
Chapter 9: Central Limit Theorem, Question 12 (pg.339) Question A balanced coin is flipped 400 times. Determine the number x such that the probability that the number of heads is between \(200 − x\) and \(200 + x\) is approximately .80. Solution Let’s first define \(n=400\) as the number of trials, \(p=0.5\) as the probability of getting a ...
1583 sym
DATA 605 - Assignment 8
Problem 11 (pg.303) A company buys 100 lightbulbs, each of which has an exponential lifetime of 1000 hours. What is the expected time for the first of these bulbs to burn out? (See Exercise 10.) Problem 10 states that the density of the minimum value is exponential with mean \(\frac{\mu}{n}\). In this case, we know that \(\mu = 1000\) and \(n=10...
2705 sym R (200 sym/9 pcs)
DATA 605 - Week 8 Discussion
Chapter 7: Sums of Random Variables, Question 11 (pg.291) Question Assume that you are playing craps with dice that are loaded in the following way: faces two, three, four, and five all come up with the same probability \(\frac{1}{6} + r\). Faces one and six come up with probability \(\frac{1}{6} − 2r\), with \(0 < r < .02\). Write a computer ...
1852 sym R (2054 sym/7 pcs) 2 img
DATA 605 - Assignment 7
Problem 1 Let \(X_1\), \(X_2\)…\(X_n\) be \(n\) mutually independent random variables, each of which is uniformly distributed on the integers from 1 to \(k\). Let \(Y\) denote the minimum of the \(X_i\)s. Find the distribution of \(Y\). Let \(j\) be a value within the range \([1,k]\). We will define the probability of \(Y=j\) as: \[P(Y=j) = \fr...
4593 sym R (678 sym/22 pcs)
DATA 605 - Week 7 Discussion
Chapter 5: Distributions and Densities, Section 1- Important Distributions, Question 18 (pg.199) Question A baker blends 600 raisins and 400 chocolate chips into a dough mix and, from this, makes 500 cookies. a. Find the probability that a randomly picked cookie will have no raisins. b. Find the probability that a randomly picked cookie will hav...
1692 sym R (570 sym/13 pcs)
DATA 605 - Assignment 6
Problem 1 A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places. numR <- 54 numW <- 9 numB <- 75 allMarbles <- numR+numW+numB probRorB <- (numR+numB...
6584 sym R (3265 sym/32 pcs) 1 img
DATA 605 - Week 6 Discussion
Chapter 3: Combinatorics, Question 9 (pg.89) Question A more refined inequality for approximating \(n!\) is given by \[\sqrt{2\pi n}(\frac{n}{e})^ne^{\frac{1}{12n+1}}<n!< \sqrt{2\pi n}(\frac{n}{e})^ne^{\frac{1}{12n}}\] Write a computer program to illustrate this inequality for \(n\) = 1 to 9. Solution First we will define our function using th...
413 sym R (2793 sym/3 pcs)
DATA 605 - Assignment 5
Choose independently two numbers, \(B\) and \(C\), at random from the interval \([0,1]\) with uniform density. Prove that \(B\) and \(C\) are proper probability distributions. Note that the point \((B,C)\) is then chosen at random in the unit square. First, we will define our interval values and simulate the draw of \(B\) and \(C\) from a uniform...
914 sym R (1507 sym/17 pcs) 2 img
DATA 605 - Week 5 Discussion
Chapter 1: Discrete Probability Distributions, Question 6 (pg.13) Question In Las Vegas, a roulette wheel has 38 slots numbered 0,00,1,2,…36. The 0 and 00 slots are green and half of the remaining 36 slots are red and half are black. A croupier spins the wheel and throws in an ivory ball. If you bet $1 on red, you win $1 if the ball stops in a...
831 sym R (617 sym/6 pcs)