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PCS 125
Midterm Part 2
Winter 2017

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This document is authorized for use only by Karol Bahnan ([email protected]). Downloaded
from www.eTutorCloud.com with permission from instructor: Alpha Education Group
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Alpha Education Group
PCS 125
Midterm Part 2
Winter 2017

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Alpha Ed
y
This document is authorized for use only by Akashdeep Warriach ([email protected]).
Downloaded from www.eTutorCloud.com with permission from instructor: Alpha Education Group
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Alpha Education Group
PCS 125
Midterm Part 1
Winter 2017

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Al
Ryerson University
Lab 7  MTH 514  Fall 2015
1. The voltage across a 1 resistor is a uniform random variable on the
interval [0, 1]. The instantaneous power is Y = X 2 . Find the c.d.f. FY (x)
and the p.d.f. fY (x) of Y .
Solution Notice that 0 Y 1, the
Ryerson University
Lab 4  MTH 514  Fall 2015
1. The number of messages sent per hour over a computer network has the
following distribution:
x
pX (x)
10
0.08
11
0.15
12
0.30
13
0.20
14
0.20
15
0.07
a) Find the expected value of the number of messages se
Ryerson University
Lab 10  MTH 514  Fall 2015
1. Flip a coin twice. On each flip, the probability of heads equals p. Let Xi
equal the number of heads (either 0 or 1) on flip i. Let W = X1 X2 and
Y = X1 + X2 . Find pW,Y (w, y) and pW/Y (w/y).
Solution
No
Ryerson University
Lab 9  MTH 514  Fall 2015
1. The pair of random variables (X, Y ) has joint p.m.f.:
pX,Y
x = 1
x=1
y=0
1/4
0
y=1
1/8
1/2
y=2
0
1/8
Find:
a) P [X 1, Y 0.5].
b) The margin p.m.f. pX (x) and pY (y).
Solution
a) P [X < 1, Y 0.5] = pX,Y (1
Ryerson University
Lab 1  MTH 514  Fall 2015
1. A manufacturer of front lights for automobiles tests lamps under a high
humidity, high temperature environment using intensity and useful life as
the responses of interest. The following table shows the pe
Ryerson University
Lab 12  MTH 514  Fall 2015
1. Queries presented to a computer database are a Poisson process of rate
= 6 queries/min. An experiment consists in monitoring the database for
m minutes and recording Nm , the number of queries presented.
Ryerson University
Lab 6  MTH 514  Fall 2015
1. Suppose that X is a continuous random variable with density function
Kx 3 x 5
fX (x) =
0 otherwise
a) Find the value of constant K.
b) Find the probability P (X < 4).
c) Find the probability that X is smal
Ryerson University
Lab 2  MTH 514  Fall 2015
1. Mobile telehpones perform handoffs as they move from cell to cell. During
a call, either performs zero handoffs(H0 ), one handoff (H1 ), or more than
one handoff( H2 ). In addition, each call is either lon
Ryerson University
Lab 11  MTH 514  Fall 2015
1. Random sample distribution
Let (Xn ) be a sequence of independent random variables with the same
probability distribution, E(Xn ) = and V ar(Xn ) = 2 and define the
sample average as:
n
X
n = 1
Xk
X
n
k=1
Ryerson University
Lab 8  MTH 514  Fall 2015
1. Assume that in the detection of a digital signal the background noise
follows a normal distribution with a mean of 0 volt and standard deviation
of 0.45 volt. The system assumes a digital 1 has been transm
Ryerson University
Lab 3  MTH 514  Fall 2015
1. A discrete random variable X has probability mass function:
C(2x + 1) x = 0, 1, 2, 3, 4
p(x) =
0
otherwise
a) Compute the value C.
b) Compute P (X = 4).
c) Find the probability that the random variable tak
Ryerson University
Lab 5  MTH 514  Fall 2015
1. It can take up to four days after you call for service to get your computed
repaired. The computer company charges for repairs according to how
long you have to wait. The number of days D until the service
Department of Physics
Course Number
Course Title
Semester/Year
Instructor
TA Name
PCS125
Physics: Waves and Fields
Alexandre (Sasha) Douplik
Kenneth Webster
Lab/Tutorial Report No.
4
Report Title
The Charge to mass ratio of an Electron
Section No.
Group N
1
Summary
The purpose of this experiment was to determine the steam quality using the raw
experimental data recorded in Table 1. It was designed to demonstrate the change in water from a
liquid to a gas due to heat gain and then return to a liquid due to
Department of Physics
Course Number
Course Title
Semester/Year
Instructor
TA Name
PCS125
Physics: Waves and Fields
Alexandre (Sasha) Douplik
Kenneth Webster
Lab/Tutorial Report No.
Report Title
Section No.
Group No.
Submission Date
Due Date
Student Name
A
Department of Physics
Course Number
Course Title
Semester/Year
Instructor
TA Name
125
PCS
Winter/2017
G. Todd Springer
Entezari Niloufar
Lab/Tutorial Report No.
05
Report Title
The Current Balance
Section No.
Group No.
Submission Date
Due Date
42
Student
Objective
The purpose of this lab is to study the magnetic forces produced by electric currents in straight, parallel
wires at a fixed separation using Amperes. Amperes law states that the magnetic field around a current
carrying wire is proportional to t
Department of Physics
Course Number
Course Title
Semester/Year
Instructor
TA Name
PCS125
Physics: Waves and Fields
Alexandre (Sasha) Douplik
Kenneth Webster
Lab/Tutorial Report No.
Report Title
Section No.
Group No.
Submission Date
Due Date
Student Name
A
Objective
The purpose of this lab is to study the magnetic forces produced by electric currents in straight, parallel
wires at a fixed separation using Amperes. Amperes law states that the magnetic field around a current
carrying wire is proportional to t
1
Summary
The purpose of this lab was to study the relationship between pressure and temperature
for saturated steam. By keeping the volume constant throughout the experiment, it was possible
to analyze how the change in temperature affects the pressure.
ii
Summary
A Venturi flow meter was used to study the volume flow rate inside a pipe, using the Bernoulli
Equation and the continuity equation for incompressible flow. The area of the entry point of the Venturi
is greater than the area at the throat, indi
ii
Summary
The purpose of the lab was to study the dynamic viscosity of a fluid and how it affects an
objecting flowing through it. The experiment consisted of three balls of varying sizes placed into
the fluid. Using the different size spheres provided a
Emma Dawson 500628685
Wednesday July 12, 2017
Lab Abstract One
Error in Simple Measurements
Objective: the objective of this experiment is to test our ability to take measurements of
objects and use the measurements to determine the mass and density of ea
Figure 1  Part 1 Collected Data  Pressure vs. Time (440 Hz)
Figure 2  Part 1 Collected Data  Pressure vs. Time (442 Hz)
Figure 3  Part 1  Amplitude vs. Time 440 Hz
Figure 4  Part 1  Amplitude vs. Time  442 Hz
Figure 5  Part 2 Collected Data  Pr