Mathematical Methods for Physicists: A concise introduction - Site Map

PROBLEMS
Figure 14.7.
The above three de®nite integrals can be evaluated by making numerical approximations.
A short table of the values of the integral
F…x† ˆ 1 Z x
p e t2 dt ˆ 1 Z
1 x
p e t2 dt
2
2 2
0
is included in Appendix 3. A more complete table can be found in Tables of
Normal Probability Functions, National Bureau of Standards, Washington, DC,
1953.
x
The Maxwell±Boltzmann distribution
Another continuous distribution that is very important in physics is the Maxwell±
Boltzmann distribution
r
a
f …x† ˆ4a x 2 e ax2 ; 0 x < 1; a > 0; …14:45†
where a ˆ m=2kT, m is the mass, T is the temperature (K), k is the Boltzmann
constant, and x is the speed of a gas molecule.
Problems
14.1 If a pair of dice is rolled what is the probability that a total of 8 shows?
14.2 Four coins are tossed, and we are interested in the number of heads. What
is the probability that there is an odd number of heads? What is the probability
that the third coin will land heads?
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