Publications by Joey Bochnik

Week 9 Homework Assignment

24.03.2024

Problem 1 Page 363 #11 The price of one share of stock in the Pilsdorff Beer Company (see Exer- cise 8.2.12) is given by Yn on the nth day of the year. Finn observes that the differences Xn = Yn+1 − Yn appear to be independent random variables with a common distribution having mean μ = 0 and variance σ2 = 1/4. If Y1 = 100, estimate the probabil...

3470 sym

Page 339 Number 11

20.03.2024

Page 339 Number 11 Write a computer program to simulate 10,000 Bernoulli trials with probabil- ity .3 for success on each trial. Have the program compute the 95 percent confidence interval for the probability of success based on the proportion of successes. Repeat the experiment 100 times and see how many times the true value of .3 is included with...

385 sym R (1104 sym/4 pcs)

Week 8 Homework

16.03.2024

Page 303 Problem 11 A company buys 100 light bulbs, 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.) We have 100 Light bulbs with an expoential lifetime of 1000 hours. This means that the Expected lifetime of the light bulbs is 1000 hours: \(E[X]=1000\) h...

2975 sym

Week 8 Discussion

14.03.2024

Page 303 Problem 11 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.) We have 100 Lightbulbs with an expoential lifetime of 1000 hours. This means that the Expected lifetime of the lightbulbs is 1000 hours: \(E[X]=1000\) hour...

762 sym

Week 7 Homework

10.03.2024

Problem 1 Let X1, X2, . . . , Xn 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 Xi’s. Find the distribution of Y. We are trying to find the distribution of Y and Y is equal to the minimum of the Xi’s This means that Y must be less than or equal to t...

4860 sym

Week 7 discussion Page 199 Question 13

07.03.2024

Page 199 Probelm 13 The Poisson distribution with parameter λ = .3 has been assigned for the outcome of an experiment. Let X be the outcome function. Find P (X = 0), P (X = 1), and P (X > 1). The Posison Distribution is given by: \(P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}\) So, to find \(P(x=0)\) we need to calculate: \(P(x=0)=\frac{.3^0e^{-.3}}{0!...

581 sym

Week 6 Homework

03.03.2024

Problem 1 A bag contains 5 green and 7 red jellybeans. How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? There are 2 scenarios where we have less than 2 green jelly beans: 5 red 0 green 4 red 1 green For the first one we can find the number of ways by calculating \(\binom{5}{0...

6678 sym

Week 6 Discussion Post

29.02.2024

Page 88 problem 5 There are three different routes connecting city A to city B. How many ways can a round trip be made from A to B and back? How many ways if it is desired to take a different route on the way back? We have 3 different routes connecting the 2 cities A and B. Each trip is the event and on each trip we have 2 choices: 1.) The route we...

1064 sym

Week 5 Assignment

25.02.2024

Problem 1: (Bayesian). A new test for multinucleoside-resistant (MNR) human immunodeficiency virus type 1 (HIV-1) variants was recently developed. The test maintains 96% sensitivity, meaning that, for those with the disease, it will correctly report “positive” for 96% of them. The test is also 98% specific, meaning that, for those without the d...

11046 sym

Week 5 Discussion post

21.02.2024

Page 36 # 9 A student must choose exactly two out of three electives: art, French, and mathematics. He chooses art with probability 5/8, French with probability 5/8, and art and French together with probability 1/4. What is the probability that he chooses mathematics? What is the probability that he chooses either art or French? We have: \(P(Art) =...

1229 sym