HW2 solutions - Physics 4120 Spring 2008 Homework #2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 4120 Spring 2008 Homework #2 Solutions 1) a) If the drunk is back at the lamp post, that means that the number of steps to the right and to the left are the same, and half the total number of steps. So we just evaluate equation 1.2.6 for n 1 = n 2 = N/2 and p=q=1/2: ( 29 ( 29 2 ! 2 / ! 2 1 ) ( N N return W N N = b) In order to return to the lamp post, the number of steps to the left and to the right must be equal. The total number of steps is thus twice the number of steps to the right, which must be an even number since we can only take an integer number of steps to the right or left. If N is odd, the drunk cannot be back at the lamp post. So the probability for odd N is exactly 0. 2) a) Note that we are interested in the limit when both p << 1 and n << N ln(1- p ) N-n = ( N-n ) ln(1- p ) exact N ln(1- p ) approximation 1, because n << N ln(1- p ) N-n - Np approximation 2, because p << 1 Take the exponent of both sides, and we get our answer: (1- p ) N-n e- Np b) ) 1 )...( 2 )( 1 ( )! ( ! +--- =- n N N N N n N N If n << N , then every term in this product is close to N , so we can approximate each term as N . There are n terms in this product, so n N n N N - )! ( !...
View Full Document

This note was uploaded on 04/17/2008 for the course PHYS 4120 taught by Professor Vajk during the Spring '08 term at Missouri (Mizzou).

Page1 / 3

HW2 solutions - Physics 4120 Spring 2008 Homework #2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online