using r language Write a function to generate a random sample of size n from the distribution with pdf,f(x)=2П2sin² x,0 < x < π.

code r: generate_random_sample <- function(n) { cdf <- function(x) { (2 / pi) * (x -…

Answered: Write a function to generate a random…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 5P

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(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.
(Practice) Determine names for functions that do the following: a. Find the average of a set of numbers. b. Find the area of a rectangle. c. Find the minimum value in a set of numbers. d. Find the density of a steel door. e. Sort a set of numbers from lowest to highest
(Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.
(Probability) The probability that a phone call will last less than t minutes can be pproximated by the exponential probability function: Probability that a call lasts less than t minutes=1et/a aistheaveragecalllength.eisEulersnumber( 2.71828). For example, assuming the average call length is 2 minutes, the probability that a call will last less than 1 minute is calculated as 1e1/2=0.3297. Using this probability equation, write a C++ program that calculates and displays a list of probabilities of a call lasting less than 1 minute to less than 10 minutes, in 1-minute increments.
(Useful utility) Modify the program written for Exercise 3 to search for the first occurrence of a user-entered sequence of characters, and then replace this sequence, when it’s found in the string, with a second user-entered sequence. For example, if the entered string is Figure 4-4 illustrates the output of Program 4-2 and the user enters that 4- is to be replaced by 3-, the resulting string is Figure 3-4 illustrates the output of Program 4-2. (Only the first occurrence of the searched-for sequence has been changed.)

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Write a function to generate a random sample of size n from the distribution with pdf, f(x) = 2 П 2 sin² x, 0 < x < π.