ECE 302 Homework 5
COMER
1. (Problem 3.20) Two fair dice are tossed and we let X be the difference in the number of dots facing
up.
(a) Find and sketch the pmf of X .
(b) Find the probability that |X | k for all k.
2. When ten fair coins are ipped, the ev
ECE 302 Homework 10
COMER
1. The joint density function of X and Y is given by
fXY (x, y ) = e(x+y)
for x > 0, y > 0. Find the density function of the random variable Z = X/Y .
2. (Problem 5.95) Let X and Y be independent random variables that are uniform
ECE 302 Homework 9
COMER
1. Two people decide to meet at a certain location. If the arrival times of the two people are independent
and uniformly distributed between 12:00 noon and 1:00 pm, nd the probability that the rst to arrive
has to wait longer than
ECE 302 Homework 7
COMER
1. Suppose that the random variable X is equal to the number of hits by a certain baseball player in his
next 3 at bats. If P (X = 1) = 0.3, P (X = 2) = 0.2, and P (X = 0) = 3P (X = 3), nd E [X ].
2. A coin that when ipped comes u
ECE 302 Homework 2
COMER
1. (Problem 2.21) A die is tossed and the number of dots facing up is noted.
(a) Find the probability of the elementary events under the assumption that all faces of the die are
equally likely to be facing up after a toss.
(b) Fin
Lecture 19
Hydrogen-Like Atoms
Atoms with all but one electrons stripped
Energy level:
13.6 eV 2
En =
Z
2
n
Bohr radius:
n 2 a0
rn =
Z
Bohrs theory can be adapted to other hydrogen-like systems.
Lecture 19
Quiz
Why is the theoretically-derived value of
Lecture 15
Antimatter in the Milky Way
e + e+ +
Lecture 15
Applications in Modern Medicine
Positron Emission Tomography (PET) Scan
A medical diagnostic to study the path and location of a
position-emitting radioactive chemical that has been
injected into
Lecture 17
Details about Test #2 have been posted to
Blackboard.
Lecture 17
Radiation from the Electron
According to the classical electromagnetic theory, the electron
in a hydrogen atom produces electromagnetic radiation, just
like an oscillating electr
ECE 302 Homework 4
COMER
1. (Problem 2.46) Ordering a deluxe pizza means you have four choices from 15 available toppings.
How many combinations are possible if toppings cannot be repeated? Assume that the order in which
toppings are selected does not mat
ECE 302 Homework 3
COMER
1. (Problem 2.69) A number x is selected at random in the interval [1, 2]. Let the events A = cfw_x < 0,
B = cfw_|x 0.5| < 0.5, and C = cfw_x > 0.75. Find P (A|B ), P (B |C ), P (A|C c ), P (B |C c ).
2. (Problem 2.75) Show that P
Lecture 18
HW04 is due NOW!
Reminder: Test #2 will be on next Wed (Oct
17). See the announcement on Blackboard for
details.
Lecture 18
Motion of the Nucleus
Center of mass:
R
m0
MR = m0 r0 R =
r0
M
C.M.
Newtons law:
e2
m0 2 r0 = M 2 R =
4 0 ( R + r0 ) 2
Lecture 16
HW03 is due NOW!
HW04 has been posted.
Test #1 statistics
Average: 48
Standard deviation: 22
Your test may be picked up after class or
between 11-12 tomorrow or email me.
Test #2 will be on Oct 17 (Wed).
Lecture 16
Thomsons Model
An atom
Lecture 14
Quiz
The photoelectric effect is explained by:
1.
2.
3.
4.
5.
Quantization of mass
Quantization of electric charge
Quantization of light
Classical theory of electromagnetism
Theory of relativity
Lecture 14
Cathode Ray Revisited
Wilhelm Rntgen
Lecture 13
HW3 has been posted.
HW2 may be picked up.
Lecture 13
Quiz
J.J. Thomson is generally recognized to be the one
who:
1.
2.
3.
4.
5.
6.
Discovered the electrons.
Measured the mass of electrons.
Measured the electric charge of electrons.
Measure
Lecture 22
HW05 is due NOW!
HW06 has been posted.
Test #2 statistics:
Average: 69.3
Standard deviation: 15.2
Lecture 22
Localization of Wave Packets
Recall that the one-dimensional distribution of the wave packet
that we discussed is of the form
(x