Publications by Tony Mei
Data 605 Homework 7
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 . For 1 ≤ j ≤ k, m(j) = ((k−j+1)n−(k−j)n)/k^n Since Y is the minimum of the Xs, then in order to find the distribution function m(j) ...
2033 sym R (293 sym/22 pcs)
Data 605 Discussion 7
8) If a coin is tossed a sequence of times, what is the probability that the first head will occur after the fifth toss, given that it has not occurred in the first two tosses? The probability of getting a head after tossing a coin is ½. The complement of that is ½ as well. We will stimulate 6 tosses, with the sixth toss displaying the head....
680 sym
Data 605 Assignment 6
1) A box contains 54 red marbles, 9 white marbles, and 75 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or blue? Express your answer as a fraction or a decimal number rounded to four decimal places. 129/138 2) You are going to play mini golf. A ball machine that contains 19 green golf balls, ...
4285 sym R (1513 sym/26 pcs)
Data605 Discussion 6
Exercise 2 An automobile manufacturer has four colors available for automobile exteriors and three for interiors. How many different color combinations can he produce? Four colors for exteriors Three colors for interiors 4 * 3 4*3 ## [1] 12 There are 12 different color combinations he can produce. ...
298 sym R (12 sym/2 pcs)
Data 605 Assignment 4
Problem Set 1 # Matrix of A A <- matrix(c(1, 2, 3, -1, 0, 4), nrow = 2, byrow = TRUE) A ## [,1] [,2] [,3] ## [1,] 1 2 3 ## [2,] -1 0 4 #Transpose X <- A %*% t(A) X ## [,1] [,2] ## [1,] 14 11 ## [2,] 11 17 #Transpose Y <- t(A) %*% A Y ## [,1] [,2] [,3] ## [1,] 2 2 -1 ## [2,] 2 4 ...
463 sym R (2243 sym/25 pcs)
Data 605 Assignment3
Homework 3 Problemset #1 (1) Rank of the matrix A is 4. (2) For an m x n matrix, If m is less than n, then the maximum rank of the matrix is m. If m is greater than n, then the maximum rank of the matrix is n. If m is greater than n, the maximum rank of the matrix is n. The rank of a matrix would be zero only if the matrix had no elements. If...
829 sym 7 img
Data 605 Assignment 2
2. Problem set 2 Matrix factorization is a very important problem. There are supercomputers built just to do matrix factorizations. Every second you are on an airplane, matrices are being factorized. Radars that track flights use a technique called Kalman filtering. At the heart of Kalman Filtering is a Matrix Factorization operation. Kalman Fi...
912 sym R (1105 sym/2 pcs)
Tmei Discussion 2
C29 Doing the computations by hand, find the determinant of the matrix A A <- matrix(c(2, 3, 0, 2, 1, 0, 1, 1, 1, 2, 0, 0, 1, 2, 3, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2), nrow = 5) A ## [,1] [,2] [,3] [,4] [,5] ## [1,] 2 0 0 0 0 ## [2,] 3 1 0 1 0 ## [3,] 0 1 1 2 0 ## [4,] 2 1 2 1 1 ##...
78 sym R (318 sym/4 pcs)
Document
1. Problem set 1 Calculate the dot product u.v where u = [0.5;0.5] and v = [3;−4] u <- c(0.5,0.5) v <- c(3,-4) dot_prod <- u %*% v dot_prod ## [,1] ## [1,] -0.5 What are the lengths of u and v? Please note that the mathematical notion of the length of a vector is not the same as a computer science definition. Length of a vector We...
1836 sym R (1035 sym/9 pcs)
Data 605 Week 1 Discussion
Exercise Solution A <- matrix(c(2, -3, 4, 1, 0),nrow=5) A ## [,1] ## [1,] 2 ## [2,] -3 ## [3,] 4 ## [4,] 1 ## [5,] 0 B <- matrix(c(1, -2, -5, 2, 4),nrow=5) B ## [,1] ## [1,] 1 ## [2,] -2 ## [3,] -5 ## [4,] 2 ## [5,] 4 C <- matrix(c(-1, 3, 0, 1, 2), nrow=5) C ## [,1] ## [1,] -1 ## [2,] ...
24 sym R (486 sym/8 pcs) 1 img