Dayton Probabilistic Methods Of Signal And System Analysis Engineering Task this is a homework for Engineering Probability and Random Processes. I will upload the file for the homework as pdf. this is the link for the book that you are going to be using https://archive.org/details/CooperProbabilisticMethodsOfSignalAndSystemAnalysis3rdEd/mode/2up Homework Assignment Number 1
The completed assignment must be submitted within a single MS Word document file. This can
be accomplished by inserting the image of your handwritten work into the pages of a word
document. The images can be generated by taking pictures of your work with your phone or by
scanning the pages using a digital scanner. I need the assignments submitted in this format to
allow for my Surface notebook to use a digital marking pen while grading your work.
Chapter 1 (Total 60 points total)
Text Book Problems (54 pts)
(1) Problem 1-2.2 in the text
(2) (Section 1-4 of text) If a pair of dice are rolled, determine the probability of each of the
following events. Assume that the roll of each die is independent of the other.
(a) Obtaining a sum of 9, (b) Obtaining a sum greater than 5, (c) Obtaining an odd number
for the sum.
(3) (section 1-4 of text) In the IC box of 1-4.3 in the text it is known that 10% of the hex
inverters are bad, 15% of the dual 4-input positive-AND gates are bad, 18% of the dual J-K
flip flops are bad, 20% of the decade counters are bad, and 20% of the 4-bit shift registers are
bad.
(a) If an IC is selected at random, what is the probability that it is both a J-K flip flop and
bad?
(b) If an IC is selected at random and found to be a decade counter, what is the probability
that it is bad?
(c) If an IC is selected at random and found to be bad, what is the probability that it is a
shifter?
(4) (Section1-4 in text) A company manufactures small electric motors having horse power
ratings of .1, 0.5, or 1.0 horsepower and designed for operation with 120 V single-phase ac,
240 V single-phase ac, or 240 V three-phase ac. The motor types can be distinguished only
by their nameplates. A distributor has on hand 3000 motors in the quantities shown in the
table below.
Horsepower
120 V ac
240 V ac
240 V 3-phase
0.1
900
400
0
0.5
200
500
100
1.0
100
200
600
One motor is discovered without a nameplate. For this motor determine the probability of
each of the following events.
(a) The motor has a horsepower rating of 0.1 hp
(b) The motor is designed for 120 V single phase operation
(c) The motor is .5 hp and is designed for 240 V singe phase operation
(d) The motor is 1.0 hp and is designed for 120 V operation
(e) The motor is 240V single phase given that is 0.5 HP
(f) The motor is 0.5 HP given that it is 240V single phase
(5) Problem 1-5.2 in the text except change the space S and the event definitions for A,B, and C
as follows; S={1,4,6,8,10,12}, A={1,6,12}, B={4,8,10), C={1,4,8,12}.
(6) Problem 1-5.6 in text except change the event definitions for A and B to A={a,d,f},
B={b,d,e,f}.
(7) Problem 1-6.1 in text except change the space S and events A,B, and C to S={1,4,6,8,10,12},
A={1,6,12}, B={4,8,10) C={1,4,8,12}.
(8) Problem 1.6.2 in the text except change the events A,B, and C be defined as; Let A be the
event that a queen is drawn on the first draw, B be the event that a 10 is drawn on the second
draw, C be the event that a jack is drawn on the third draw.
MATLAB Assignment (6 Points):
Use the code I have provided in the class simulation example: “Random Selection of Resistors in
Bin” to solve the following problem. You should only have to modify the input numbers to get
what you need.
There are 1000 cookies in a large cookie bin. There are four types of cookies, each weighing a
different amount; 10, 15, 20, and 25 grams respectively. The relative number of these cookies
in the jar is as follows; 10 gram: 250, 15 gram:200, 20 gram: 150, 25 gram:400. A cookie is
drawn at random from the jar as a part of a chance experiment. If each cookie type is defined as
an event within the chance experiment, plot the relative frequency of each event as a function of
the number of trials. Compare your relative frequency to the true probability of each
event. Comment on the agreement between the two as the number of trails is increased. Provide
a copy of your code and a copy of each of your plots.
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