INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
(c) z(t) = y(t) cos(w0 t) Z(w) = 12 Y (w w0 ) + 12 Y (w + w0 ).
(i) For this case, Y (w) = 0 and therefore Z(w) = 0.
(ii) Note that Y (w w0 ) is obtained by shifting Y (w) to the right by w0 ,
and Y (w + w0 ) is obtained by shifting Y (w) to the left by w
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
it is best to avoid extended transforms as much as possible.
x1 (t) =
=
=
=
sin(t)(u(t) u(t 1)
sin(t)u(t) sin(t)u(t 1)
sin(t)u(t) sin(t 1) + )u(t 1)
sin(t)u(t) + sin(t 1)u(t 1)
The last line is obtained from the fact sin( + ) = sin().
Suppose x(t) = sin(t
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
EDU>p = [2 +3 0 0.95]
p=
2.0000 3.0000
0 0.9500
EDU> roots(p)
ans =
1.1241
0.8646
0.4887
Since it is required that 0 .95 1 , .95 = .865.
3. Suppose that Y possesses the density function
cy, 0 y 2,
f ( y) =
0, elsewhere.
a. Find the value of
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
10. The grade point averages (GPAs) of a large population of college students are approximately
normally distributed with mean 2.4 and standard deviation .8. What fraction of the students will
possess a GPA in excess of 3.0? (Hint: Answer the questi
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
(ii) If w0 wm wc < w0 , then X(w) and the filter are related as follows:
From this, we see that Y (w) has the form:
12
(iii) If wc > w0 + wm , then the passband of the lowpass filter Hc (w) includes all
the frequency content of X(w).
Therefore we see that
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
5. You want to include weight into your regression. Instead of controlling
for weight linearly, you decide to dene dummy variables for light cars
(weight <= 2500), medium cars (2500 < weight < 3500) and heavy cars
(weight >= 3500). How can you do this in
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
Question 8: For the following three molecules draw:
the Lewis dot structure (showing the valence electrons).
the twodimensional chemical structure (showing bonds between atoms and any lone pairs).
the threedimensional geometry of the molecule (nonbondin
INTRODUCTION TO NUCLEAR ENGINEERING AND RADIOLOGICAL SCIENCES
NERS 211

Spring 2015
ATOMS
Question 4: Scientists describe atoms using atomic symbols. These are written as:
A
Z
X
where X indicates the chemical element, Z is the atomic number, and A is the mass number. Write
the complete atomic symbols for the atoms in the list below, wher