Homework 2: CS 517 (Summer 2022) Due Date: 6/28/2022 For each problem involving R, you must give the commands, and corre

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Homework 2 Cs 517 Summer 2022 Due Date 6 28 2022 For Each Problem Involving R You Must Give The Commands And Corre 1 (53.6 KiB) Viewed 12 times

Homework 2: CS 517 (Summer 2022) Due Date: 6/28/2022 For each problem involving R, you must give the commands, and corresponding results as copied from R window. 1. Suppose x₁ = 1 and x₂ = 2 and x=xj-1+2/xj-1 for j = 2 to n Write a function testLoop which takes the single argument n and returns the vector x.. Test the program with n= 5, 10 and 20 2. Check whether the following can define probability distribution functions, explain your answer. a) f(x)= x/15, for x = 1,2,3,4,5 b) f(x)=(5-x2)/6, x=0,1,2,3 c) f(x)=4, x= 3,4,5,6 d) f(x) = (x+1)/25, x = 1,2,3,4,5 3. During one stage in the manufacture of integrated circuit chips, a coating must be applied. If 70% of chips receives a thick enough coating, use Tablel to find probabilities that among 15 chips: a. at least 12 will have thick enough coating b. at most 6 will have thick enough coating c. Exactly 10 will have thick enough coating. Also, for each case, run the R script to get the answer and compare with the results obtained using the table. 4. Given a random variable having the normal distribution with u = 16.2, and variance = 1.5625, find the probabilites that it will take on a value a. greater than 16.8 b. less than 14.9 c. between 13.6 and 18.8 d. between 16.5 and 16.