PHY4604
Problem Set 1
Department of Physics
Page 1 of 3
PHY 4604 Problem Set #1
Due Wednesday September 6, 2006 (in class)
(Total Points = 60, Late homework = 50%)
Reading:
Griffiths Chapter 1.
Useful Math:
)
(
2
1
2
1
1
0
2
2
+
+
∞
−
Γ
=
∫
n
n
x
a
n
a
dx
e
x
,
where
Γ
(x)
is the gamma function and
Γ
(x+1) = x
Γ
(x)
.
Γ
(1) =
Γ
(2) = 1,
Γ
(n) = (n1)! if n is a positive integer, and
π
=
Γ
)
(
2
1
.
Integration by parts:
b
a
b
a
b
a
fg
gdx
dx
df
dx
dx
dg
f
+
−
=
∫
∫
Problem 1 (12 points):
Consider a room containing 14 people, whose ages are as follows:
One person aged 14,
One person aged 15,
Three people aged 16,
Two people aged 22,
Two people aged 24,
Five people aged 25.
(a) (1 point)
If you selected one person from the room, what is the
probability
that the person’s
age would be 15?
(b) (1 point)
What is the
most probable
age?
(c) (1 point)
What is the
median
age?
(d) (1 point)
What is the
average
age?
(e) (1 point)
Let N(j) be the number of people with age j.
Histogram N(j) versus j.
(f) (2 points)
Compute <j
2
> and <j>
2
.
(g) (3 points)
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 Spring '07
 Field
 mechanics, Variance, Energy, Kinetic Energy, Work, Department of Physics

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