Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 21.1-2

POSTLUDE: SYMMETRY AND THE CONCEPTUAL FOUNDATIONS OF THERMOSTATISTICS

Physics — Statistical Mechanics · statistics-coin-toss-gaussian

Problem

Associate the value

+1

with one side of a coin (``head'') and the value

-1

with the other side (``tail''). Plot the probability of finding a given ``value'' when throwing one, two, three, four, and five coins. (Note that the probability is discrete---for two coins the plot consists of just three points, with probability

= \frac{1}{4}

for

X = \pm 1

and probability

= \frac{1}{2}

for

X = 0

.) Calculate

\sigma

for the case

n = 5

, and roughly sketch the Gaussian distribution for this value of

\sigma

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