1. Sep 1, 2009

Liketothink

1. The problem statement, all variables and given/known data
For this exercise, four coins are tossed 32 times and the number of heads are recorded for each toss. Each toss falls into one of the following macroscopic states; 0 heads, 1 heads, 2 heads, 3 heads and 4 heads. Suppose the 32 tosses result in the following outcome: 3,2,3,2,2,4,0,3,0,2,0,4,4,2,3,1,2,0,1,3,2,3,1,3,3, 2,3,2,3,3,2 and 1. Your task is to count the number of times when 1 heads, 2 heads, ... appears, and to calculate the measured and expected distribution functions.
To calculate the measured distribution function, if nj is the number of counts for jth heads for N trials, then the experimental distribution function is fj=nj/N. For example, the number of counts with zero heads is 4 giving f0=4/32=0.125.
The expected distribution for such an experiment follows a binomial distribution function and is given by
C!/(C-xj)!(xj!)(2^C)
where C is the total number of coins, xj is the number of heads. Thus for the case of 0 heads, f0=4!(4−0)!0!2^4=1/16=0.0625.

2. Relevant equations
C!/(C-xj)!(xj!)(2^C)

3. The attempt at a solution

*
o C
o 4
o 10
o 11
3
o fj
o 0.125
o 0.3125
o 0.34375
o 0.09375
o distribution
o 0.25
o 0.043945313
o 0.080566406
o #NUM!