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
have a value between 19.3 and 20.7?
2. In a random samp
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 = cfw_0, 1, 2, 3, . This is a discrete sample space.
2. Le
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 a bottle
has between 11.9 and 12.1 ounces in it). Assu
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
has between 11.9 and 12.1 ounces in it). Assuming that
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, and Var ( X 3) = 3.
(a) Find the E ( X 1 + X 2 + X 3). =
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, and Var ( X 3) = 3.
(a) Find the E ( X 1 + X 2 + X 3).
(b
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) = P (B )
(3) P (A B ) = P (A)P (B )
2. Bayes Theorem:
If
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
f (x) = (1 p)x1 p
f (xi ) = 1/n
f (x) =
x1
r1
(1 p)xr
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
1
2
1
1/8
1/4
1/8
0
1/8
1/4
1/8
1
(a) Find P (X > 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
have a value between 19.3 and 20.7? We apply the CLT,
P
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 digit can be
0,1,2,.,9. Then S is a sample space of 1000