Publications by Maliat
Discussion 2 DATA 605
R Markdown Each of the archetypes below is a system of equations with a square coefficient matrix, or is a square matrix itself. Compute the determinant of each matrix, noting how Theorem SMZD indicates when the matrix is singular or nonsingular. Archetype A, Archetype B, Archetype F, Archetype K, Archetype L A <- matrix(c(1,2,1,-1,1,1,2,1,0), ...
632 sym R (538 sym/16 pcs)
Discussion 4
R Markdown A caption # Creating matrix into S S <- matrix(c(-1,4,1,1,4,-1,5,0,1,6,-2,2,2,-1,2,5), 4,4) S ## [,1] [,2] [,3] [,4] ## [1,] -1 4 1 2 ## [2,] 4 -1 6 -1 ## [3,] 1 5 -2 2 ## [4,] 1 0 2 5 # RREF library(pracma) answer <- rref(S) answer ## [,1] [,2] [,3] [,4] ## [1,] 1 ...
312 sym R (421 sym/4 pcs) 1 img
Discussion 5 DATA 605
R Markdown Chapter-1 Exercise-3 In the early 1600s, Galileo was asked to explain the fact that,although the number of triples of integers from 1 to 6 with sum 9 is the same as the number of such triples with sum 10, when three dice are rolled, a 9 seemed to comeup less often than a 10-supposedly in the experience of gamblers. Write a program to...
775 sym R (1350 sym/18 pcs)
Data 605 Homework 6
DATA 605 Homework 6 Maliat I 9/30/2021 R Markdown 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 How many ways can 5 jellybeans be withdrawn from the bag so that the number of green ones withdrawn will be less than 2? # Combinations: (0 green + 5 green) + (1 green + 4 green) choose(5,0)*choose(7,5) + choose(5,1)*choose(7,4) ## [1] 19...
3048 sym R (2234 sym/26 pcs)
Data 605 Homework 7
Homework 7 Maliat I 10/10/2021 R Markdown 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 . A caption Your organization owns a copier (future lawyers, etc.) or MRI (future doctors). This ma...
1837 sym R (1119 sym/24 pcs) 1 img
Homework 8 Data 605
Homework 8 Maliat I 10/16/2021 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.) n=100 lifetime=1000 lifetime/n ## [1] 10 Exercise 14 Assume that X_1 and X_2 are independent random variables, each having a...
1538 sym R (157 sym/8 pcs)
Data 605 Homework 9
Week 9 Data 605 Maliat I 10/23/2021 R Markdown The price of one share of stock in the Pilsdorff Beer Company (see Exercise 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, est...
5328 sym
Discussion 9
Discussion 9 Maliat I 10/23/2021 R Markdown 9.1. BERNOULLI TRIALS pg. 337 10. Find the probability that among 10,000 random digits, the 3 appears no more than 931 times. Area under the normal curve between Z=0 and Z= 2.28 is 0.4887 using the normal distribution table to two decimal points: https://www.mathsisfun.com/data/standard-normal-distr...
773 sym R (77 sym/4 pcs)
Discussion 10
Discussion 10 Maliat I 10/28/2021 12.1/13. Use Stirling’s Formula, prove that \[ \left(\begin{array}{c} 2 n \\ n \end{array}\right) \sim \frac{2^{2 n}}{\sqrt{\pi n}} \] Stirling’s Formula: \(n ! \sim \sqrt{2 \pi n}\left(\frac{n}{e}\right)^{n}\) \[ \left(\begin{array}{c} 2 n \\ n \end{array}\right)=\frac{2 n !}{n !(2 n-n) !}=\frac{(2...
1226 sym
Homework 10
Homework 10 Maliat I 10/30/2021 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: *Th...
1013 sym R (101 sym/4 pcs)