Design a simulation exercise in r to approximate the value

Reference no: EM13117714

Polya urn simulation via R
I need help in two probability problems using R program.

1. Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( X^X) when X has a U [0,1] distribution. Plot the value of the approximation as the sample size goes from 1 to 10,000. Use the Notebook feature in RStudio to create an HTML file for your answer.

2. Simulation of a Polya Urn. Put a = 10 white balls and b = 20 blue balls in an urn. Then, randomly draw a ball from the urn, and replace it along with another ball of the same color, repeat.
a) Write an R program to simulate Rn, the proportion of white balls in the urn after n draws from the urn, for any integer n.
b) Plot the histogram of Rn for n = 1,000.
c) Simulate Rn 10,000 times.
d) Overlay the histogram with a line graph of the appropriate limiting distribution. Use the Notebook feature in RStudio to create an HTML file for your answer.

Reference no: EM13117714

Questions Cloud

Determining exponential-logarithm-power questions : Solve the following problems with exponents-Write the following numbers using scientific notation

How much heat energy, in kilojoules, is require : How much heat energy, in kilojoules, is required to convert 65.0g of ice at 18.0 degrees celcius to water at 25.0 degrees celcius.

Illustrate what is the safes coefficient of kinetic friction : The safe slides with a constant speed if Clyde pushes from behind with 420 {rm N} of force while Bonnie pulls forward on a rope with 285 {rm N} of force. Illustrate what is the safe's coefficient of kinetic friction on the bank floor?

Calculate the mole fraction, x : A gaseous mixture contains 420.0 Torr of H2(g), 391.3 Torr of N2(g), and 79.5 Torr of Ar(g). Calculate the mole fraction, X, of each of these gases.

Design a simulation exercise in r to approximate the value : Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( X^X) when X has a U [0,1] distribution. Plot the value of the approximation as the sample size goes from 1 to 10,000

Logarithm and scientific notation : Imagine that every single person in your contact list has the same number of people in their contact list as you. Write this total number of all the contacts in all the phones (ignore the fact that some may repeat) as an exponential. Next, evaluat..

What is the concentration of a solution : What is the concentration of a solution formed by diluting 25.0 mL of a 3.2 M NaCl solution to 135.0 mL.

What are some of the causes of failed change : What are some of the causes of failed change? Where possible, illustrate these with examples. What practices and/or processes might managers adopt to improve the prospect of successful change implementation?

Find out the dog resultant displacement vector : A dog searching for a bone walks 3.00 m south, then 8.20 m at an angle 30.0° north of east, and finally 14.0 m west. Find out the dog's resultant displacement vector using graphical techniques.

User Account

All Pages