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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 << 1 and the fraction of trial in which an event occurs is low n << 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 !...
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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.
- Fall '06