Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 1, Problem 1.24P
To determine
(a)
To Prove:
The relationship between Lorentz factor and β by using binomial approximation.
To determine
(b)
To Derive:
The relationship between
To determine
(c)
To Show:
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1.16. Establish thermodynamically the formulae
(F).
V
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Express the pressure P of an ideal classical gas in terms of the variables μ and T, and verify the
above formulae.
Step 1
Rewrite the original integral
Therefore,
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a² + u²
(²)
dt as
+ 16
= arctan(y) to
Step 2
Use the following integration formula for the inverse trigonometric functions.
1.20
t
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✓)) + C
(3.8) This question introduces a rather efficient method
for calculating the mean and variance of probability
distributions. We define the moment generating
function M(t) for a random variable x by
M(t) = (etx).
Show that this definition implies that
(x) = M(n) (0),
(3.51)
(3.52)
where M(n) (t)
mean (x)
= d" M/dt" and further that the
M (¹) (0) and the variance σ
=
=
M(2)(0) [M(¹) (0)] 2. Hence show that:
-
(a) for a single Bernoulli trial,
=
M(t) pe 1-p;
(3.53)
(b) for the binomial distribution,
M(t) = (pe +1 - p)";
(3.54)
(c) for the Poisson distribution,
M(t) = em(et-1);
(3.55)
(d) for the exponential distribution,
λ
M(t)
(3.56)
Hence derive the mean and variance in each case
and show that they agree with the results derived
earlier.
Chapter 1 Solutions
Modern Physics For Scientists And Engineers
Ch. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3PCh. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Prob. 1.7PCh. 1 - Prob. 1.8PCh. 1 - Prob. 1.9PCh. 1 - Prob. 1.10P
Ch. 1 - Prob. 1.11PCh. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Prob. 1.21PCh. 1 - Prob. 1.22PCh. 1 - Prob. 1.23PCh. 1 - Prob. 1.24PCh. 1 - Prob. 1.25PCh. 1 - Prob. 1.26PCh. 1 - Prob. 1.27PCh. 1 - Prob. 1.28PCh. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Prob. 1.31PCh. 1 - Prob. 1.32PCh. 1 - Prob. 1.33PCh. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - Prob. 1.39PCh. 1 - Prob. 1.40PCh. 1 - Prob. 1.41PCh. 1 - Prob. 1.42PCh. 1 - Prob. 1.43PCh. 1 - Prob. 1.44PCh. 1 - Prob. 1.45PCh. 1 - Prob. 1.46PCh. 1 - Prob. 1.47PCh. 1 - Prob. 1.48PCh. 1 - Prob. 1.49PCh. 1 - Prob. 1.50PCh. 1 - Prob. 1.51PCh. 1 - Prob. 1.52PCh. 1 - Prob. 1.53P
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