Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345: Quiz 4 Take home, due May 3 Name:
1. A variable X has mean = 20 and = 4. If a random sample of size n = 49 is
taken from the population, what is the probability that the sample mean, X will
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345 Practice Exam 1 Solutions
1. An experiment involves counting the number of insectdamaged leaves on a plant.
Find the sample space of this experiment. What type of sample space is this?
S = c
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345 Solutions Practice Exam 2
1. A machine that fills bottles of Coca Cola is within tolerance 98% of the time (although
not necessary to complete this problem, assume that within tolerance means
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345 Practice Exam 2
1. A machine that fills bottles of Coca Cola is within tolerance 98% of the time (although
not necessary to complete this problem, assume that within tolerance means a bottle
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345 Practice Exam 3
1. Suppose that we have three independent random variables, X1, X2 and X3.
Further suppose: E ( X 1) = 2, Var ( X 1) = 1 , E ( X 2) = 5, Var ( X 2) = 4 , and
E ( X 3) = 10, an
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345 Practice Exam 3
1. Suppose that we have three independent random variables, X1, X2 and X3.
Further suppose: E ( X 1) = 2, Var ( X 1) = 1 , E ( X 2) = 5, Var ( X 2) = 4 , and
E ( X 3) = 10, an
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345: Quiz 1 Based on 2.52.7 Name:
Formulas you may need:
1. Independence: Two events are independent if any one of the following equivalent statement is true:
(1) P (AB ) = P (A)
(2) P (B A) =
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Here are the probability mass functions of a uniform distribution, binomial distribution, geometric distribution and negative binomial distribution, but not in the above
orders.
n
x
f (x) =
px (1 p)nx
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345: Quiz 3 Based on 5.1,5.3 and 5.5 Name:
Recall:
Cov (X, Y ) = E (XY ) E (X )E (Y )
X,Y =
Cov (X, Y )
,
X Y
1. Suppose that the random variables X, Y have the following joint distribution
x\y
0
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
Stat 345: Quiz 4 Take home, due May 3 Name:
1. A variable X has mean = 20 and = 4. If a random sample of size n = 49 is
taken from the population, what is the probability that the sample mean, X will
Elements of Mathematical Statistics and Probability Theory
STAT 345

Fall 2012
21.
Let "a", "b" denote a part above, below the specification
S = cfw_ aaa, aab, aba, abb, baa, bab, bba, bbb
26.
A vector with three components can describe the three digits of the ammeter. Each di