# hw1_f10 - Physics 112, Fall 2010: Holzapfel Problem Set 1...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 112, Fall 2010: Holzapfel Problem Set 1 (7 problems). Due Monday, September 6, 5 PM Problem 1 : Sharpness of the multiplicity function . Suppose you flip 10000 coins. Let P ( n ) represent the probability that exactly n coins come up heads. a) What is the probability, P(5000), of getting 5000 heads and 5000 tails? b) What is the relative probability P(5100)/P(5000) of getting 5100 heads and 4900 tails? c) What is the relative probability P(6000)/P(5000) of getting 6000 heads and 4000 tails? d) Repeat the previous calculation for only 10 coins. What is the relative probability, P(6)/P(5), of getting 6 heads? Problem 2 : Poisson Distribution . The Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate, and are independent of the time since the last event. a) Show that the probability P(n) that an event characterized by probability p occurs n times in N trails is given by the now familiar binomial distribution. P ( n ) = N ! ( n ) ! ( N- n ) ! p n ( 1- p ) N- n . (1) b) Now consider a situation where the probability of an event is low p &lt;&lt; 1 and the fraction of trial in which an event occurs is low n &lt;&lt; N . An example would be the emission of alpha particles by a weak radioactive source. Show that the expression found in a) becomes: P ( n ) = n n !...
View Full Document

## This note was uploaded on 11/18/2010 for the course PHYSICS 112 taught by Professor Steveng.louie during the Fall '06 term at University of California, Berkeley.

### Page1 / 3

hw1_f10 - Physics 112, Fall 2010: Holzapfel Problem Set 1...

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

View Full Document
Ask a homework question - tutors are online