Means and Variances for some commonly used
distributions
Distribution
Mean
Variance
Bernoulli-
(1 )
Binomial B (n, )
n
n(1 )
Poisson Po()
Uniform U (a, b)
a +b
2
Normal N (, 2 )
(ba)2
12
2
Standard No
MATHS 2201 Engineering Mathematics IIA
Assignment 1, 2013
Due: 5:00pm, Tuesday 19 March (week 3) 2013.
1. A recent study found that 17.8% of passenger vehicles had defective tyres and 13.0%
had defect
Practice Questions
Digital Systems (ELEC ENG 2100)
Last revised: February 21, 2017
These exercises are intended to reinforce the learning outcomes from ELEC ENG 2100 Digital Systems.
Many of the exerc
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 9, Week 10
1. Consider the initial value problem
y 00 + xy 0 + (2x2 + 1)y = 0,
y(0) = 1,
y 0 (0) = 1.
(1)
(a) Find the first six terms of the power
MATHS 2201 Engineering Mathematics I Tutorial Exercise 1
Week of 5 March 2012
1. A pair of fair dice are rolled and the total of the two faces is calculated.
(a) Write down the sample space for this e
MATHS 2201 Engineering Mathematics I Tutorial Exercise 1
Week of 5 March 2012
1. A pair of fair dice are rolled and the total of the two faces is calculated.
(a) Write down the sample space for this e
MATHS 2201 Engineering Mathematics I Tutorial Exercise 4
Week of 26 March 2012
1. For each of ten streets with bicycle lanes, investigators measured the distance between the centre
line and a cyclist
MATHS 2201 Engineering Mathematics I Tutorial Exercise 3
Week of 19 March 2012
1. The paper Ultimate Load Capacities of Expansion Anchor Bolts (J. Engr. Energy, 1993, pp.
139-158) reports the followin
MATHS 2201/7201, Engineering Mathematics IIA
Tutorial 10, Week 11
1. Consider the function f (x) = | sin x| for < x < and f (x + 2) = f (x) for all x.
Sketch the function and find its Fourier series.
MATHS 2201/7201, Engineering Mathematics IIA
Tutorial 6, Week 7
1. The functions y1 (x) = 1, y2 (x) = sin x and y3 (x) = cos x are all solutions of the third-order
ODE
y (3) + y 0 = 0
(1)
for < x < .
MATHS 2201 Engineering Mathematics IIA Tutorial 2
1. Suppose the diameters of pistons produced by a certain manufacturer are normally distributed
with mean 120mm and standard deviation 0.2mm. The diam
MATHEMATICS IB - SEMESTER 1, 2012
Tutorial 3 Algebra Solutions
ALGEBRA
Problem: A vector u is said to be orthogonal to a subspace V Rn if u is orthogonal to every v V . Prove that u
is orthogonal to V
MATHEMATICS IB - SEMESTER 2, 2012
Tutorial 4 Solutions
ALGEBRA
Question:Let V be a subspace of Rn and u a vector in Rn . We showed in lectures that we can
write u = w1 + w2 , where w1 V and w2 is orth
MATHS 2201 Engineering Mathematics IIA Tutorial Exercise 1
1. In cars with ABS brakes, faults occasionally occur with the wheel sensors and a warning light is
illuminated. It can also happen that the
MATHS 2201 Engineering Mathematics I Tutorial Exercise 4
Week of 26 March 2012
1. For each of ten streets with bicycle lanes, investigators measured the distance between the centre
line and a cyclist
MATHS 2201 Engineering Mathematics I Tutorial Exercise 2
Week of 12 March 2012
1. Suppose the diameters of pistons produced by a certain manufacturer are normally distributed
with mean 120mm and stand
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 8, Week 9
1. A simple model for torsional oscillation of a suspension bridge (such as the Tacoma Narrows
bridge) consists of a rigid rod of mass m a
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 6, Week 7
1. The functions y1 (x) = 1, y2 (x) = sin x and y3 (x) = cos x are all solutions of the third-order
ODE
y (3) + y 0 = 0
(1)
for < x < . Ca
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 11, Week 12
1. By solving for each of the three cases > 0, = 0, and < 0, show that the eigenvalues
of the boundary value problem
X 00 X = 0,
X 0 (0)
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 10, Week 11
1. Consider the function f (x) = | sin x| for < x < and f (x + 2) = f (x) for all x.
Sketch the function and find its Fourier series.
2.
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 11, Week 12
1. By solving for each of the three cases > 0, = 0, and < 0, show that the eigenvalues
of the boundary value problem
X 00 X = 0,
X 0 (0)
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 6, Week 7
1. The functions y1 (x) = 1, y2 (x) = sin x and y3 (x) = cos x are all solutions of the third-order
ODE
y (3) + y 0 = 0
(1)
for < x < . Ca
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 5, Week 6
1. Flow out of Torrens Lake is controlled by a sluice gate, which can be raised to create
an opening at the bottom through which water can
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 5, Week 6
1. Flow out of Torrens Lake is controlled by a sluice gate, which can be raised to create
an opening at the bottom through which water can
MATHS 2201 Engineering Mathematics I Tutorial Exercise 3
Week of 19 March 2012
1. The paper Ultimate Load Capacities of Expansion Anchor Bolts (J. Engr. Energy, 1993, pp.
139-158) reports the followin
MATHS 2201/7201, Engineering Mathematics 1
Tutorial 9, Week 10
1. Consider the initial value problem
y 00 + xy 0 + (2x2 + 1)y = 0,
y(0) = 1,
y 0 (0) = 1.
(a) Find the first six terms of the power seri
MATHS 2201 Engineering Mathematics I Tutorial Exercise 2
Week of 12 March 2012
1. Suppose the diameters of pistons produced by a certain manufacturer are normally distributed
with mean 120mm and stand
MATHS 2201/7201, Engineering Mathematics IIA
Tutorial 8, Week 9
1. A simple model for torsional oscillation of a suspension bridge (such as the Tacoma Narrows
bridge) consists of a rigid rod of mass m
THE UNIVERSITY OF ADELAIDE
SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING
GEOTECHNICAL ENGINEERING II (C&ENVENG 2069)
ASSIGNMENT No. 2, 2013
COMPACTION and VERTICAL STRESS IN SOILS
Deadline: 5 pm, Thur