Publications by Susanna Wong
DATA 605 Homework 8
Problem 1 (Section 7.2 Exercise 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.) For exercise 10, it says “Let \(X_{1}\), \(X_{2}\), · · · , \(X_{n}\) be \(n\) independent random variables each of which has an expon...
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DATA 605 Homework 7
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 . Commutative Distribution Function of Y Let \(Y=min(X_{1},X_{2},\cdots ,X_{n})\) \(P(Y\leq y)=1-P(Y> y)\) \(P(Y\leq y)=1-P(X_{1}>y,X_{2}>...
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DATA 605 Homework 6
Question 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? We should consider 2 cases: (1) The number of green jellybeans withdrawn is 0. (2) The number of green jellybeans withdrawn is 1. Case 1: The number of green jellybeans with...
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DATA 605 Homework 5
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 di...
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DATA 605 Discussion 5
Question Exercise 2.2.22 Write a program to carry out the following experiment. A coin is tossed 100 times and the number of heads that turn up is recorded. This experiment is then repeated 1000 times. Have your program plot a bar graph for the proportion of the 1000 experiments in which the number of heads is \(n\), for each \(n\) in the interval ...
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R Markdown hwllo #remove.packages("rsconnect") #Remove Installed Packages #remotes::install_version("rsconnect", version = "0.8.29")...
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R Markdown This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com. When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the...
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