Q1: A knight in standard international chess is sitting on a board as follows Th

Question

Q1: A knight in standard international chess is sitting on a board as follows

The knight starts on square "0" and makes T jumps to other squares according to the allowable moves in Chess (so that at each space, it has between two to four valid moves). The knight chooses amongst the allowable moves at each jump uniformly at random and keeps track of the running sum S of keys on which it lands. See below for specific questions and answers.

1.After T=16 moves, what is the mean of the quantity S modulo 13?

2.What is the standard deviation?

3.After T=512 moves, what is the mean of the quantity S modulo 311?

4.What is the standard deviation?

5.After T=16 moves, what is the probability that the sum is divisible by 5, given that it is divisible by 13?

6.After T=512 moves, what is the probability that the sum is divisible by 7, given that it is divisible by 43?

Explanation / Answer

using System; using System.Linq; using System.IO; class Program { static void Main(string[] args) { string[] dirfiles = Directory.GetFiles("c:\sri\"); var avg = dirfiles.Select(file =>new FileInfo(file).Length).Average(); avg = Math.Round(avg / 10, 1); Console.WriteLine("The Average file size is {0} MB",avg); Console.ReadLine(); } }

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.