Math 3215
Intro. Probability & Statistics
Summer 14
Quiz 2
Answer the questions. Be sure to justify your answer do not simply write the answer down.
Use complete sentences where appropriate and scrap paper if needed (on the desk at the front
of class, scr
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
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 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 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 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
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 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 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
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
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
Math 3215
Intro. Probability & Statistics
Summer 14
Group Quiz 6
You may work in groups, ask the instructor for the help, use books or notes or the internet.
Any calculator can be used on this quiz.
1. Let W1 , W2 be independent random variables with the
Math 3215
Intro. Probability & Statistics
Summer 14
Practice Exam 3: Solutions
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
Math 3215
Exam 2
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
Exam 1
Summer 2014
Instructor: Sal Barone (B)
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 full
Math 3215
Intro. Probability & Statistics
Summer 14
Practice Exam 2
1. What are the mean and variance of the Gamma distribution with parameters and ?
Solution: The mean is = and the variance is 2 = 2 .
2
2. Describe in three sentences or less the relation
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
Quiz 3
Answer the questions. Be sure to justify your answer do not simply write the answer down.
Use complete sentences where appropriate and scrap paper if needed (on the desk at the front
of class, scr
Math 3215
Intro. Probability & Statistics
Summer 14
Quiz 1
Answer the questions. Be sure to justify your answer do not simply write the answer down.
Use complete sentences where appropriate and scrap paper if needed (on the desk at the front
of class, scr
Math 3215
Intro. Probability & Statistics
Summer 14
Quiz 4
Answer the questions. Be sure to justify your answer do not simply write the answer down.
Use complete sentences where appropriate and scrap paper if needed (on the desk at the front
of class, scr
Math 3215
Intro. Probability & Statistics
Summer 14
Quiz 5
1. A certain fast food chain is doing a promotion where whenever you buy a hamburger you get
one of three stickers, and if you collect all three stickers you win free hamburgers for a year.
Suppos
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