Math 3215
Intro. Probability & Statistics
Summer 14
Homework 5b: Due 7/10/14
1. Let X1 , X2 , X3 be a random sample from a distribution with p.d.f. f (x) = 2e2x , 0 < x < .
This means that X1 , X2 , X3 are independent random variables each with the same p
Math 3215
Intro. Probability & Statistics
Summer 14
Practice Exam 1
1. Exploring: probability, distribution, random variable, expectation. Consider the space which
consists of the rst 6 letters of the alphabet S = cfw_a, b, c, d, e, f . What does it mean
Math 3215
Intro. Probability & Statistics
Summer 14
Practice Exam 3
1. Consider the function f (x, y) = (x + 2y) if 0 < x, y < 1 and f (x, y) = 0 otherwise. Find a
value such that f is a joint p.d.f. Is this choice unique? Find the marginal p.d.f.s of X a
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 5: Due 7/3/14
1. Let X and Y be continuous random variables with joint/marginal p.d.f.s
0 x y 1,
f (x, y) = 2,
f1 (x) = 2(1 x),
0 x 1,
f2 (y) = 2y,
0 y 1.
1
2
Find the conditional p.d.f. h(y|x)
Math 3215
Intro. Probability & Statistics
Summer 14
Practice Exam 2
1. What are the mean and variance of the Gamma distribution with parameters and ?
2. Describe in three sentences or less the relationship between the Exponential distribution,
Poisson dis
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 4: Due 6/26/14
1. Let the joint p.m.f. of X and Y be dened by
f (x, y) =
x + 2y
,
33
x = 1, 2, y = 1, 2, 3.
Find the marginal p.d.f. of X and that of Y . Find P (X > Y ), P (Y > X) and P (X + Y
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 3b: Due 6/19/14
1. Dene what it means for X to be a continuous random variable. How is the probability
density function f (x) used to calculate P (X x)? What does the distribution function F (x)
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 2: Due 6/5/14
1. Let X be a random variable with binomial distribution b(n, p), which means that the space of
X is S = cfw_0, 1, 2, . . . , n and the p.m.f. f (x) is f (x) = n px (1 p)nx . Show
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 1b: Due 5/29/14
1. You roll two dice. Let X denote the sum of the dice. Compute the probability mass function
f (x) and plot a probability histogram.
Solution: The space of X is S = cfw_2, 3, .
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 3: Due 6/12/14
1. You do not need to justify your answer to this question. List, without proof, the p.m.f., mean,
and variance of the random variable X where X has the following distributions: n
Math 3215
Exam 3
Summer 2014
Instructor: Sal Barone
Name:
GT username:
1. No books or notes are allowed.
2. You may use ONLY NON-GRAPHING and NON-PROGRAMABLE scientic calculators. All other electronic devices are not allowed.
3. Show all work and fully ju
Math 3215
Intro. Probability & Statistics
Summer 14
Homework 1: Due 5/22/14
1. A four sided die is rolled 25 times and the following numbers are recorded:
4, 3, 2, 3, 1, 3, 1, 2, 1, 1, 3, 4, 2, 4, 1, 2, 2, 4, 4, 1, 2, 2, 3, 3, 4.
Construct a table showing
1. Integrate
ln(x2/3 )
dx.
x
2. Find the particularsolution y = f (x) which satises the separable dierential
equation 2y x = e xy and y(1) = 0.
3. Let R be the region bounded by one arc of the secant curve y = sec x, < x < ,
2
2
and the line y = 2.
(i) Fi
Math 1501
Calculus I
Fall 13
Practice Exam 1
1. Find the domain of
x
. Express your answer in interval notation.
x
x2
2. Is the function f (x) one-to-one?
f (x) =
x3 + 1 if x < 0
2x
if x 0
3. Write the domain and range of f (x) = |x + 2| 1 in interval no
Math 1501
Calculus I
Fall 13
Practice Exam 3
1. Show that f (x) =
3
4x2 +2
satises f (x) = O(1).
2. Find the particular solution to the separable dierential equation y =
fying f (0) = 3.
x
y
satis-
2
3. Let R be the region bounded by the curves y = x2 (x
Math 1501
Calculus I
Fall 13
Practice Exam 2
1. Find
dy
dx
if y = cosx (x).
2x3/2
.
x2 + 1
2. Use the properties of natural log to simplify rst, then nd y where y = ln
3. A triangle with hypotenuse length 5, height 4 and base x is shrinking as
How fast is
Math 1501 Calc I
Fall 2013
Lesson 9 - Lesson 20
Instructor: Sal Barone
School of Mathematics
Georgia Tech
August 19 - August 6, 2013
(updated October 4, 2013)
L9: D IFFERENTIATION RULES
Covered sections: 3.3 & 3.5
Exam 1 (L1-L8) Tuesday, September 10 (tom
Math 1501 Calc I
Fall 2013
Lesson 21 - Lesson 36
Instructor: Sal Barone
School of Mathematics
Georgia Tech
October 7 - November 13, 2013
(updated November 18, 2013)
L21: R IEMANN SUMS & T HE DEFINITE INTEGRAL
Covered sections: 5.1 & 5.3
Exam 2 (L9-L20) Th
Math 1501 Calc I
Fall 2013
Lesson 1 - Lesson 8
Instructor: Sal Barone
School of Mathematics
Georgia Tech
August 19 - August 6, 2013
(updated September 1, 2013)
F IRST DAY
Syllabus, homework set, practice quizzes & exams
http:/people.math.gatech.edu/sbar