Publications by William Aiken
WAIKEN_HW1_DATA605
Introduction: One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors. For this assignment, build the first letters for both your first and last name using point plots in...
1531 sym R (1530 sym/7 pcs) 5 img
WAIKEN_HW10_DATA605
Smith is in jail and has 1 dollar; he can get out on bail if he has 8 dollars. A guard agrees to make a series of bets with him. If Smith bets A dollars, he wins A dollars with probability .4 and loses A dollars with probability .6. Find the probability that he wins 8 dollars before losing all of his money if (a) he bets 1 dollar each time (timid...
1396 sym R (438 sym/3 pcs)
WAIKEN_DATA605_HW8
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? mu = 1000 n = 100 E = mu/n E ## [1] 10 Assume that X1 and X2 are independent random variables, each having an exponential density with parameter λ. Show that Z = X1 − X2 has density f...
1189 sym R (214 sym/10 pcs)
WAIKEN_HW5_DATA605
(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 disease, 9...
4598 sym R (1186 sym/57 pcs)
WAIKEN_HW4_DATA605
Introduction With the attached data file, build and visualize eigen imagery that accounts for 80% of the variability. Provide full R code and discussion. Method We first download the data file and visualize one of the images. What the heck type of shoe is this? test <- readJPEG("/Users/williamaiken/Downloads/jpg/RC_2500x1200_2014_us_53446.jpg"...
1220 sym R (1378 sym/12 pcs) 5 img
WAIKEN_HW3_PS1&2
Problem Set 1 1. What is the rank of the matrix \(A\)? \[\begin{equation} A= \begin{pmatrix} 1 & 2 & 3 & 4\\ -1 & 0 & 1 & 3\\ 0 & 1 & -2 & 1\\ 5 & 4 & -2 & -3 \end{pmatrix} \end{equation}\] The rank of a matrix is the dimension of the span of the column vectors. Let \(\vec v_1, \vec v_2, \vec v_3, \vec v_4\) denote the colum...
4125 sym
WAIKEN_HW6_DATA605
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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2?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 two possible proportions that satisfy the less than 2 requirement: * 6 red jellybeans/7 total jellybeans * 7 red jellybeans/7 total jellybeans one_green <- choose(5,1) *...
3877 sym R (1071 sym/24 pcs)
WAIKEN_HW7_DATA605
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 . expanded solution Y = 1 is k^n − (k − 1)^n Your organization owns a copier (future lawyers, etc.) or MRI (future doctors). This machine h...
1695 sym R (315 sym/24 pcs)
WAIKEN_HW9_DATA605
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 probability that Y365 is ≥...
2537 sym R (151 sym/6 pcs)
WAIKEN_HW15_DATA605
Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. ( 5.6, 8.8 ), ( 6.3, 12.4 ), ( 7, 14.8 ), ( 7.7, 18.2 ), ( 8.4, 20.8 ) ref_site sum_xy = 5.6 * 8.8 + 6.3 * 12.4 + 7 * 14.8 + 7.7 * 18.2 + 8.4 * 20.8 sum_x = 5.6 + 6.3 + 7 + 7.7 + 8.4 sum_x2 = 5.6^2 + 6.3^2 + 7^2 + 7.7^2 +...
3230 sym R (550 sym/6 pcs)