📗 Enter your ID (the wisc email ID without @wisc.edu) here: and click (or hit enter key) 1,2,3,4,5,6,7,8,9,10p5
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📗 Create a vector of Fibonacci numbers and a lower triangular matrix with Binomial coefficients.
📗 Fibonacci numbers have the property that \(F_{i} = F_{i-1} + F_{i-2}\) with \(F_{1} = F_{2} = 1\). Details see: Wikipedia.
📗 Binomial coefficients have the property that \(B_{i,j} = B_{i-1,j} + B_{i-1,j-1}\) with \(B_{i,1} = B_{i,i} = 1\) for each \(i = 1, 2, 3, ...\). Details see: .
📗 Note: you can use the tril function in MATLAB to get the lower triangular part of a matrix, details see: Doc.
📗 Note: you are allowed to use permutation formula, but it is highly recommended that you do not use it, and use the above recurrence relation instead, for this question.
📗 Simulate loaded dice throw and stop until you get \(n\) "\(x\)"s. Create a matrix with 2 rows, the first row contains random numbers between 0 and 1, and the second row contains the numbers on the dice corresponding to the random numbers in the first row based on the inverse transform method. Use the value of \(n\) and \(x\) and probabilities specified in each question. Enter the matrix you created.
📗 Inverse transform sampling samples a random variable with cumulative density by finding \(x = F^{-1}\left(u\right)\) where \(u\) is a uniform random number between 0 and 1. Details see: Wikipedia.
📗 Aside: the only possible fair dice (having faces with the same shape and size) have four, six, eight, twelve or twenty faces. Details see: Wikipedia.
📗 Create a vector representing a deck of \(n\) cards. Use the value \(1\) to represent a card facing up and \(0\) to represent a card facing down. Start with all cards facing up and you flip all cards at positions that are divisible by some integers. For example, flipping positions that are divisible by \(2\) means flipping the \(2\)nd, \(4\)th, \(6\)th, ... cards, and flipping positions that are divisible by \(3\) means flipping the \(3\)rd, \(6\)th, \(9\)th, ... cards. Use the size of the deck and the list of integer divisors specified in each question. Enter the vector representing the cards after you finish flipping the cards in the text box below each question.
📗 Note: a positive number has an odd number of divisors if and only if it is a perfect square. Details see: Wikipedia.
📗 [1 point] Create the vector representing ??? cards (initially facing up) after flipping all cards at positions that are divisible by ???. Clarification: this means flipping the cards divisible by ??? first, then flipping the cards divisible by ??? next, then flipping the cards divisible by ???, and so on.
📗 [1 point] Create the vector representing ??? cards (initially facing up) after flipping all cards at positions that are divisible by ???. Clarification: this means flipping the cards divisible by ??? first, then flipping the cards divisible by ??? next, then flipping the cards divisible by ???, and so on.
📗 [1 point] Please enter any comments and suggestions including possible mistakes and bugs with your version of the questions and the auto-grading, and materials relevant to solving the question that you think are not covered well during the lectures. If you have no comments, please enter "None": do not leave it blank.
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📗 Please submit your code (.m, .txt, or .pdf are all acceptable) on Canvas Assignment P5.
📗 Your coding style and technique will not be graded, but please consider the following:
(1) Add comments to describe what the code is doing.
(2) Indent "for" loops and "if" blocks.
(3) Use descriptive but short variable names.
(4) Add white spaces and/or blank lines for readability.
📗 It is highly recommended that you use the commands and functions from the lectures, but you are allowed to use any built-in MATLAB commands and functions.
(1) Please do not use the example solution as the starter code. You should write all the code yourself and only use the example solution as a reference when you get stuck.
(2) Please do not use the example solution as a guide for coding style. It is written so that it only solves a specific version of the problems. You code should be more general: you should define variables for constants, define functions for repetitive actions, and use descriptive variable names.
📗 Please report possible mistakes in the solution, and if you have better (shorter or more efficient) ways of solving the same problem, you can share your code on Piazza (but please do so after the due dates).
📗 If you use one or more lines of code from the example solution, other students in the class, or code you found on the Internet, you must give attribution by putting a comment at the beginning of your code submission, for example:
% Code attribution: P5 example solution.
% Code attribution: (student name)'s P5 solution.
% Code attribution: (student name)'s answer on Piazza: (link to Piazza post).
% Code attribution: (person name)'s answer on Stack Overflow: (link to page).