Name _
Tuesday, March 26, 2013
MATH 511
Quiz 8
Show Your Work
No Calculators
1. If X has an exponential distribution with E ( X ) = 4 , then
P ( X > 8 ) = _ (Answer in terms of e)
Solution: P ( X > 8 ) = e
8 4
=
1
.
e2
2. Suppose that the life of a partic
Math 511
Review For Exam 2
Of course, you should go over your notes and all the problems assigned on problem sets
6 10 or discussed in class. The problems on the exam will all be based on those
assigned for homework,
Name _
Thursday, March 28, 2013
MATH 511
Quiz 9
Show Your Work
No Calculators
1. Suppose that X is an exponential random variable with mean 2.
What is the expected value of Y = 3 X + 2 X 3 ?
Hint: The moment generating function for X is M ( t ) = (1 t ) .
Math 511 Review for Exam 3
1. Suppose that Y is a random variable having mean 10, variance 8, and moment
generating function H(t). Suppose that the moment generating function for X
is M (t ) = e4 t H ( 3t ) . Find the mean and variance for X.
2. Suppose t
Math 511
Review Exam #1
Of course, you should go over your notes and all the problems assigned on problem sets
1 5 or discussed in class. The problems on the exam will all be based on those assigned
for homework, discussed in class, on the quizzes, on thi
Math 511 Review for Exam 3
1. Suppose that Y is a random variable having mean 10, variance 8, and moment
generating function H(t). Suppose that the moment generating function for X
is M (t ) = e4 t H ( 3t ) . Find the mean and variance for X.
2
Solution:
Name _
4/7/13
Math 511
Practice Exam #3
1. Suppose that a bus arrives at its destination at a random time between 9:00 and 9:12. Let
X denote the number of minutes after 9:00 that the bus arrives.
2 =
(a). E ( X ) =
(b). P( X < 5 | X > 2) =
2. Let X be a
Name _
March 7, 2013
Math 511
Exam #2
Show All Work
1. A package of 200 seeds contains 40 that are defective and will not grow (the rest are fine).
Suppose that you choose a sample of 10 seeds from the box without replaceme
Name _
March 7, 2013
Math 511
Practice Exam #2
Show All Work
1. A box of 40 apples contains 10 that are rotten and 30 that are OK. Suppose that you choose a
sample of 8 apples from the box without replacement.
Let X denote the number of rotten apples in t
Name _
April 11, 2013
Math 511 Exam #3
Show All Work
1. (a). Suppose that a company manufactures bags of peanuts whose weight is
normally distributed with a mean of 40 grams and a standard deviation of 5.
Let X denote the weight of a particular bag of pea
Name _
Math 511
Exam #1
Show All Work
No Calculators
1. Suppose that A and B are events in a sample space S and that P(A) = 0.4 and
P(B) = 0.6 and P(A|B) = 0.3. Suppose too that B, C, and D are mutually independent
events and P(C) = 0.7 and P(D) = 0.8
Wha
Name _
Thursday February 7, 2013
Math 511
Exam 1
Show All Work
1. Suppose that A, B are events in the sample space S with
P ( A ) = 0.4, P ( B | A ) = 0.3, P ( A | B ) = 0.6
[Express all answers as decimals or frac
Name _
March 7, 2013
Math 511
Practice Exam #2
Show All Work
1. A box of 40 apples contains 10 that are rotten and 30 that are OK. Suppose that you choose a
sample of 8 apples from the box without replacement.
Let X denote the number of rotten apples in t
Name_
Math 511
Practice Exam #1B
Show All Work
No Calculators
1. (a). Suppose that A, B and C are events in a sample space S and that
P( A) = 0.4, P( B ) = 0.3, P( A B) = 0.5 , P(C) = 0.7
What is the value of:
(i). P( A B ) = _
Solution:
First note that P
Name _
Thursday, April 4, 2013
MATH 511
Quiz 10
Show Your Work
No Calculators
1. Suppose that X, Y are continuously distributed with joint pdf given by
30 xy 2 , x 1 y 1 x, 0 x 1
f ( x, y ) =
elsewhere
0,
3
1
(a). P X , Y =
4
4
Solution:
3
1
3
1
4
4
P X
Name _
4/10/13
Math 511
Practice Exam #3
1. Suppose that a bus arrives at its destination at a random time between 9:00 and 9:12.
Let X denote the number of minutes after 9:00 that the bus arrives.
2 =
(a). E ( X ) =
(b). P( X < 5 | X > 2) =
Solution:
0 +