SAMPLE PROBLEMS FOR FINAL EXAM
MATH 627 Probability, 12/13
1. Find the probability that a hand of ve cards from a deck of 52 cards
contains exactly two distinct pairs and three hearts.
2. Let X and Y be jointly normal random variables with parameters
X =
SAMPLE PROBLEMS FOR EXAM I
MATH 627 Probability, 9/13
1. Find the probability that a hand of seven cards contains exactly two
distinct pairs.
2. A fair die is rolled three times. Let X be the smallest number that
occurs in the three rolls. Find P (X = 4).
Probability
1.1
1.2
1.3
1.4
1.5
1.6
1. 1
p
BASIC CONCEPTS
PROPERTIES OF PROBABILITY
METHODS OF ENUMERATION
CONDITIONAL PROBABILITY
INDEPENDENT EVENTS
BAYES'S THEOREM
BASIC CONCEPTS
It is usually difficult to explain to the general public what statistician
SAMPLE Problem Solutions
MATH 627 Probability, 12/13
Beware of the answers given below.
1. Let C (n, r) =
(13,
n!
. CC (522)99 .
r!(nr)!
,5)
2
2. Compute E [Y |X = 6.3] and Y |X and use these values for a normal
distribution.
3.
5!5!
10!
4. X is approxima
SAMPLE PROBLEMS FOR EXAM II
MATH 627 Probability, 11/13
1. Let X and Y be random variables with the joint probability density
function
fXY (x, y ) =
6 2 xy
(x + )
7
2
0
0 < x < 1, 0 < y < 2
otherwise
1
Find P (X > Y ) and P (Y > 2 |X = 1 ).
2
2. Let X and