Publications by Joey Bochnik
Week 10 Discussion
Page 415 problem 15 Write a program to simulate the outcomes of a Markov chain after n steps, given the initial starting state and the transition matrix P as data (see Ex- ample 11.12). Keep this program for use in later problems. markov_chain <- function(initial_state, transition_matrix, n_steps) { current_state <- initial_state # Iterate thro...
759 sym Python (2990 sym/24 pcs)
Week 9 Homework Assignment
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...
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Page 339 Number 11
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
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...
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Week 8 Discussion
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...
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Week 7 Homework
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...
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Week 7 discussion Page 199 Question 13
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!...
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Week 6 Homework
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...
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Week 6 Discussion Post
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...
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Week 5 Assignment
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...
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