Math 1690
Solutions Exam 3a (orange)
Oct 26, 2005
Problem 1 Suppose that S = cfw_a, b, c, d, e, f is the sample space for an experiment and that E = cfw_c, d and
F = cfw_a, d, f are events.
(a) Are the events E and F mutually exclusive? (briey explain y
Math 1690
Solutions Exam 3b (purple)
Oct 26, 2005
Problem 1 Suppose that S = cfw_a, b, c, d, e, f is the sample space for an experiment and that E = cfw_a, c, f and
F = cfw_b, d are events.
(a) Are the events E and F mutually exclusive? (briey explain y
Math 1690
Exam 4a
Nov 16, 2005
Name :
Instructions: Justify all answers. An answer without any justication will receive no credit.
Problem 1
The probability distribution of a random variable X is shown in the accompanying table:
x
P(X = x)
-10
.20
-5
.15
Math 1690
Exam 4b
Nov 16, 2005
Name :
Instructions: Justify all answers. An answer without any justication will receive no credit.
Problem 1
The probability distribution of a random variable X is shown in the accompanying table:
x
P(X = x)
-20
.1
-15
.25
Math 1690
Exam 5a
Dec 5, 2005
Name :
Instructions: Justify all answers. An answer without any justication will receive no credit.
Problem 1
3 x2
(a) Show that the function f (x) = 2
0
random variable X .
for 1 x 1
is a probability density function for so
Math 1690
Make Up Exam
Dec 7, 2005
Name :
Instructions: Justify all answers. An answer without any justication will receive no credit.
4
Problem 1
Use a table of integrals to evaluate
1
dx
.
x2 16 x2
Problem 2 Suppose that S = cfw_a, b, c, d is the sample
Math 1690
Solutions Exam 1a (Peach)
Sept 7, 2005
1
Problem 1
x dx.
Compute the value of
0
A solution :
1
x dx =
0
Problem 2
12
x
2
1
=
x=0
12 12
1
1 0= .
2
2
2
xex dx.
Use integration by parts to nd the indenite integral
A solution : Let u = x and dv = ex
Math 1690
Solutions Exam 1b (Yellow)
Sept 7, 2005
2
Problem 1
x dx.
Compute the value of
1
A solution :
2
1
Problem 2
1
x dx = x2
2
2
=2
1
1
3
=.
2
2
Use integration by parts to nd the indenite integral
A solution : Let u = ln x and dv = x dx then du =
x
Math 1690
Solutions Exam 2a (purple)
Sept 30, 2005
Problem 1
25x2 + y 2 .
(a) Compute f (1, 0) if f (x, y ) =
f (1, 0) =
A solution :
(b) Find the domain of g (s, t) =
25 = 5.
4 s2 t2 .
A solution : Need 4 s2 t2 0 or, equivalently, s2 + t2 4. Geometricall
Math 1690
Solutions Exam 2b (white)
Sept 30, 2005
Problem 1
(a) Compute g (1, 1) if g (x, y ) =
xy
.
x2 + y 2 + 1
A solution :
g (1, 1) =
(b) Find the domain of h(u, v ) =
11
= 1/3.
12 + 12 + 1
1
.
u+v1
A solution : Need u + v 1 = 0 or, equivalently, u +
Math 1690
Solutions Exam 2a (purple)
Sept 30, 2005
Problem 1
25x2 + y 2 .
(a) Compute f (1, 0) if f (x, y ) =
f (1, 0) =
A solution :
(b) Find the domain of g (s, t) =
25 = 5.
4 s2 t2 .
A solution : Need 4 s2 t2 0 or, equivalently, s2 + t2 4. Geometricall
Math 1690
Solutions Exam 1b (Yellow)
Sept 7, 2005
2
Problem 1
x dx.
Compute the value of
1
A solution :
2
1
Problem 2
1
x dx = x2
2
2
=2
1
1
3
=.
2
2
Use integration by parts to nd the indenite integral
A solution : Let u = ln x and dv = x dx then du =
x
MATH 1690 PRACTICE EXAM 1
Please read the directions carefully and show all work.
1. (20 points) You have won a lottery that will pay you $5000 a year for 20 years.
two friends make you offers. Albert offers to pay you $100,000 now if you will
sign to rig
Math 1690
Solutions Exam 1a (Peach)
Sept 7, 2005
1
Problem 1
x dx.
Compute the value of
0
A solution :
1
x dx =
0
Problem 2
12
x
2
1
=
x=0
12 12
1
1 0= .
2
2
2
xex dx.
Use integration by parts to nd the indenite integral
A solution : Let u = x and dv = ex
Math 1690
Solutions Exam 2b (white)
Sept 30, 2005
Problem 1
(a) Compute g (1, 1) if g (x, y ) =
xy
.
x2 + y 2 + 1
A solution :
g (1, 1) =
(b) Find the domain of h(u, v ) =
11
= 1/3.
12 + 12 + 1
1
.
u+v1
A solution : Need u + v 1 = 0 or, equivalently, u +
Math 1690
Solutions Exam 3a (orange)
Oct 26, 2005
Problem 1 Suppose that S = cfw_a, b, c, d, e, f is the sample space for an experiment and that E = cfw_c, d and
F = cfw_a, d, f are events.
(a) Are the events E and F mutually exclusive? (briey explain y
STEP 1
What does it contain?
PP thH
STEP 2
SIMPLE VARIABLE
SQUARE VARIABLE ADD
SQUARE VARIABLE SUBTRACT
SU BTRACT SQUARE VARIABLE
EXPONENTIAL AND LOGARITHMS
What does it contain? Match the list numberfrom STEP 1.
1.
a+bx
I) fa-fbxdx
2