There is more than one way to calculate the value of T. One way that this can be done is by generating random numbers. This works by recognizing that if you take a unit square that you can draw a quarter circle of unit radius inside the square. The area of the quarter circle is exactly π/4 and the area of the square is 1. So if you randomly generate a pair of uniform numbers between 0 and 1 they will be distributed uniformly across the square. If you count the total number of points generated and the number of points (x, y) where x² + y² = r² < 1 then the ratio of those two numbers will tend towards the ratios of the areas of the square and the circle as the number of points generated increases. The ratio of the areas is just π/4 so if you take that ratio and multiply it by 4 you get an estimate for T. a) Write code to estimate 7 using this method. You can generate random numbers in the range 0

There is more than one way to calculate the value of T. One way that this can be done is by generating random numbers. This works by recognizing that if you take a unit square that you can draw a quarter circle of unit radius inside the square. The area of the quarter circle is exactly π/4 and the area of the square is 1. So if you randomly generate a pair of uniform numbers between 0 and 1 they will be distributed uniformly across the square. If you count the total number of points generated and the number of points (x, y) where x² + y² = r² < 1 then the ratio of those two numbers will tend towards the ratios of the areas of the square and the circle as the number of points generated increases. The ratio of the areas is just π/4 so if you take that ratio and multiply it by 4 you get an estimate for T. a) Write code to estimate 7 using this method. You can generate random numbers in the range 0

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: In cryptography, it is important to use prime numbers. Write a function is_prime that has a…

A: Program description: num is the user input integer variable used to check whether the number is…

Q: m + n = 2k + 2k = 4k therefore adding even numbers always gives an even number. The above is wrong…

A: Yes , As we know that adding of two even is always a even number

Q: %matplotlib inline import numpy as np from matplotlib import pyplot as plt from math import sin,…

A: Explanation:Integrand Function: The function integrand(u) computes…

Q: A school has been selling raffle tickets to raise funds for the school library. Each ticket is sold…

A: Raffles are a popular fundraising method for schools and organizations, as they can generate…

Q: Children often play a memory game in which a deck of cards containing matching pairs is used.The…

A: The objective of the question is to create a program that simulates a memory game. The game involves…

Q: Given L = {w = [a, b]*: |w| is even}, the correct statements are: (aa Uab U ba U bb)* is a regular…

A: Regular Languages:Regular languages are a fundamental class of languages in formal language theory.…

Q: Q10: Using (ode45, ode23, or ode15s), solve the below dynamic electrical system differential…

A: Hello student

Q: Convert to Reverse Octal:

A: I have provided PYTHON CODE along with CODE SCREENSHOT and OUTPUT SCREENSHOT...

Q: We expect the closed form solution have a polynomial function by n. The first step to find the…

A: We need to solve multiple equations to find the values of variables

Q: Start with any positive number n. If n is even divide it by 2, if n is odd multiply by 3 and add 1.…

A: We need to write a code for the given scenario. *Language used is C++.

Question

There is more than one way to calculate the value of T. One way that this can be done is by generating random numbers. This works by recognizing
that if you take a unit square that you can draw a quarter circle of unit radius inside the square.
The area of the quarter circle is exactly π/4 and the area of the square is 1.
So if you randomly generate a pair of uniform numbers between 0 and 1 they will be distributed uniformly across the square. If you count the total
number of points generated and the number of points (x, y) where x² + y² = ² < 1 then the ratio of those two numbers will tend towards the
ratios of the areas of the square and the circle as the number of points generated increases. The ratio of the areas is just π/4 so if you take that ratio
and multiply it by 4 you get an estimate for .
a)
b
Write code to estimate π using this method. You can generate random numbers in the range 0<x< 1 using:
import random.
x = random.random()
You'll want to generate around 1000 pairs. Store your x and y values as you go along, computing running totals of how many points you have
generated and how many fall within the circle - so that you can compute a running estimate of as the number of iterations increases.
Then make two plots.
The first plot should show the running fraction difference of the estimate from the value of math.pi (so is x is the estimate you should be computing:
(x-T)/T). It should look something like this:

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Algorithm of the program:

VIEW

Step 2: Source Code of the above program:

VIEW

Step 3: Screenshot of the above code:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n2)
Find the value of the Bresenham's circle drawing method's decision parameter p. Step-by-step instructions are given for how Bresenham's method for making a circle works.
You are asked to determine the value of the decision parameter p used in Bresenham's circle drawing algorithm. The algorithm for drawing circles by Bresenham is presented in a series of instructions.
Students in a basic statistics class are allowed to take as much time as needed on their final exam. The exact amount of time it takes each student to finish the final exam is an example of a discrete random variable continuous random variable
A popular word game involves finding words from a grid of randomly generatedletters. Words must be at least three letters long and formed from adjoining letters.Letters may not be reused and it is valid to move across diagonals. As an example,consider the following 4 * 4 grid of letters: A B C DE F G HI J K LM N O P The word “FAB” is valid (letters in the upper left corner) and the word “KNIFE”is valid. The word “BABE” is not valid because the “B” may not be reused. Theword “MINE” is not valid because the “E” is not adjacent to the “N”. Write a program that uses a 4 * 4 two-dimensional array to represent the gameboard. The program should randomly select letters for the board. You may wishto select vowels with a higher probability than consonants. You may also wish toalways place a “U” next to a “Q” or to treat “QU” as a single letter. The programshould read the words from the text file words.txt (included on the website withthis book) and then use a recursive algorithm to…
One way to do multiplication is by repeated addition. For example, 47 x 25 can be evaluated as 47 +47 +47 +...+47 (25 times). Sketch out an algorithm for multiplying two positive numbers a and b using this technique.
In python