Question

A Monte Carlo simulation is a method for finding a value that is difficult to compute...

A Monte Carlo simulation is a method for finding a value that is difficult to compute by performing many random experiments. For example, suppose we wanted to estimate π to within a certain accuracy. We could do so by randomly (and independently) sampling n points from the unit square and counting how many of them are inside the unit circle (assuming that the probability of selecting a point in a given region is proportional to the area of the region). By assuming we actually get the expected number, we can solve for π.

(a) Describe a reasonable sample space to model this experiment.

(b) Let N be the number of sample points that are inside the unit circle. Find E(N).

(c) Use this to construct a random variable P with E(P) = π. This random variable will give your estimate of π.

(d) Find the variance of P.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
This problem is also a Monte Carlo simulation, but this time in the continuous domain: must...
This problem is also a Monte Carlo simulation, but this time in the continuous domain: must use the following fact: a circle inscribed in a unit square has as radius of 0.5 and an area of ?∗(0.52)=?4.π∗(0.52)=π4. Therefore, if you generate num_trials random points in the unit square, and count how many land inside the circle, you can calculate an approximation of ? For this problem, you must create code in python (A) Draw the diagram of the unit square...
You are using a Monte Carlo simulation to estimate the area of shape inside a unit...
You are using a Monte Carlo simulation to estimate the area of shape inside a unit square by taking n sample points. How big does n have to be in order for the estimate to be within about ±0.01 of the correct answer? I believe this has to do with binomial distribution.
Perform Monte-Carlo estimation where theta = E(e^U) where U is a continuous uniform random variable between...
Perform Monte-Carlo estimation where theta = E(e^U) where U is a continuous uniform random variable between zero and one a. Estimate !using 1000 data points and obtain a 95% confidence interval for this case. b. Perform part a) 100 times. Check how often the true !actually does fall within the 100 resulting confidence intervals. Please solve in R.
Conducting a Simulation For example, say we want to simulate the probability of getting “heads” exactly...
Conducting a Simulation For example, say we want to simulate the probability of getting “heads” exactly 4 times in 10 flips of a fair coin. One way to generate a flip of the coin is to create a vector in R with all of the possible outcomes and then randomly select one of those outcomes. The sample function takes a vector of elements (in this case heads or tails) and chooses a random sample of size elements. coin <- c("heads","tails")...
Phone calls can be classified as voice (V) if someone is speaking, or data (D) if...
Phone calls can be classified as voice (V) if someone is speaking, or data (D) if there is a modem or fax transmission. Based on many observations made by the telephone company, we have the following probability model: P [V] = 0.8, P [D] = 0.2. Data calls and voice calls are produced independently. The random variable Kn is the number of data calls in a collection of n calls telephone (a) What is the E [K100], the expected number...
This worksheet is about doing simulations on a TI-83/84, but feel free to do the work...
This worksheet is about doing simulations on a TI-83/84, but feel free to do the work on a computer if you prefer. You are going to estimate the value of ? through a simulation. A circle inscribed in a 1x1 square has area ?/4 (you may want to draw a picture to convince yourself of this). Now, we can simulate picking points inside the square as follows: randomly select a value between 0 and 1 to be the x-coordinate, and...
In Mississippi, a random sample of 110 first graders revealed that 48 of them have been...
In Mississippi, a random sample of 110 first graders revealed that 48 of them have been to a dentist at least once. (a) Find a 95% confidence interval for the population proportion of first-graders in Mississippi who have been to a dentist at least once. Enter the smaller number in the first box. Confidence interval: ( , ). College officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. A 9898% confidence interval...
Problem 1: Relations among Useful Discrete Probability Distributions. A Bernoulli experiment consists of only one trial...
Problem 1: Relations among Useful Discrete Probability Distributions. A Bernoulli experiment consists of only one trial with two outcomes (success/failure) with probability of success p. The Bernoulli distribution is P (X = k) = pkq1-k, k=0,1 The sum of n independent Bernoulli trials forms a binomial experiment with parameters n and p. The binomial probability distribution provides a simple, easy-to-compute approximation with reasonable accuracy to hypergeometric distribution with parameters N, M and n when n/N is less than or equal...
You plan to invest $4 million in the construction of an oil well which has a...
You plan to invest $4 million in the construction of an oil well which has a potential yearly revenue of $10 million. The oil well will be located in the Golf of Mexico. As we all know, this region is constantly hit by hurricanes. Assuming that if during an entire year there is a hurricane, this will disrupt your production and your well will lose 20% its yearly production. And if during a year there are two hurricanes, your well...
2) Airline accidents: According to the U.S. National Transportation Safety Board, the number of airline accidents...
2) Airline accidents: According to the U.S. National Transportation Safety Board, the number of airline accidents by year from 1983 to 2006 were 23, 16, 21, 24, 34, 30, 28, 24, 26, 18, 23, 23, 36, 37, 49, 50, 51, 56, 46, 41, 54, 30, 40, and 31. a. For the sample data, compute the mean and its standard error (from the standard deviation), and the median. b. Using R, compute bootstrap estimates of the mean, median and 25% trimmed...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT