Stat 3611
Midterm 2, Spring 2014
ID
Name
Instructions:
You have 50 minutes to complete this exam.
Write answers in the space provided below each question. If you need more room, you can
use the back of the page, but clearly indicate where this is done.
Stat 3611 Homework 1, Spring 2015
Due in class on Friday, Jan. 30, 2015
1. Let f (x, y) be a function defined by
(
x2 + y , x = 0, 1, 2 and y = 3, 4
f (x, y) =
0,
otherwise
Find out
P
(a)
x f (x, 4);
P 2
(b)
y y f (1, y);
P P
(c)
x
y 4f (x, y).
2. Find th
Stat 3611 More Practice Problems
Internet ID:
Name:
1. Three students are selected at random from a chemistry class and classied as male or female.
(a) List the elements of the sample space S1 , using the letter M for male and F for female.
(b) Dene a sec
If A1 , A2 , . . . , An are a partition of sample space
S, then P (A1 A2 An ) = P (A1 ) + P (A2 ) +
+ P (An ) = P (S) = 1.
P (A B C) = P (A) + P (B) + P (C) P (A
B) P (A C) P (B C) + P (A B C).
If A and A are complementary events, then
P (A) + P (A )
Stat 3611 In-class Quiz 7
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Name:
1. The amount of the time that a train travels between two stations is random variable with
mean = 25 minutes and a standard deviation = 3 minutes. Each day there are 36
scheduled train services between the two
Stat 3611 In-class Quiz 6
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Name:
1. If X is a continuous uniform random variable on the interval [1, 4]. What is the probability
that X is smaller than 2, P (X < 2)?
2. Given a standard normal distribution, nd the area under the curve that lie
Stat 3611 In-class Quiz 5
Internet ID:
Name:
1. A random variable X has the probability distribution function f (x) as
x
1
f (x) 0.2
2
0.1
3
0.5
4
0.2
(a) What is the expected value of X?
(b) What is the variance of X?
2. A random variable Y has the proba
Stat 3611 In-class Quiz 3
Internet ID:
Name:
1. Mike decides to go out for dinner. He will go to one of the two restaurants nearby. The
rst restaurant has 4 appetizers, 5 entries, and 3 desserts. The second restaurant has 5
appetizers, 6 entries, and 2 de
Stat 3611 In-class Quiz 2
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Name:
1. List the elements of each of the following sample spaces:
(a) the set S = cfw_x|2x 4 0 and x < 5;
(b) the set of integers between 1 and 50 divisible by 9.
2. Jim lives in City A. He plans to visit his friend
Stat 3611 Homework 2, Spring 2015
Due in class on Feb. 9
Show all the work. 40% of the points will be taken off if only
the final answer is shown without intermediate steps.
1. Exercise 2.6.
2. Exercise 2.10.
3. Exercise 2.14.
4. Exercise 2.16.
5. Exercis
Stat 3611 In-class Quiz 1
Internet ID:
Name:
1. Suppose a function f (x, y) is dened as f (x, y) = xy for x = 0, 1, 2; y = 4, 5 and f (x, y) = 0
otherwise. Compute
x2 f (x, y)
x
2. Compute the integral
3
xex dx
2
3. Compute the derivative
d
dx
3x2
+ xex
5
Generalized Multiplication Rule
The multiplication rule can be generalized to any number of
operations.
Rule 2.2
Generalized Multiplication Rule
If an operation can be performed in n1 ways, and if for each of these a
second operation can be performed in
Stat 3611 (Spring 2014)
Chapter 2
Yang Li
University of Minnesota Duluth
Yang Li (UMD)
Stat 3611
1 / 13
Chapter 2
2.1: Sample Space
2.2: Events
2.3: Counting Sample Points
2.4: Probability of an Events
2.5: Additive Rules
2.6: Conditional Probabilit
Stat 3611
Name
Midterm 1, Spring 2014
ID
solution
Instructions: You have 50 minutes to complete this exam. Write answers in the space provided below
each question. If you need more room, you can use the back of the page, but clearly indicate where this
is
Stat 3611 Homework 7, Spring 2014
Due in class on Apr. 02, 2014
1. For n = 6 and p = 1/2, we have
(a) P (2 X 5) = P (X 5) P (X 1) = 0.9844 0.1094 = 0.875.
(b) P (X < 3) = P (X 2) = 0.3438.
2. From Table A.1 with n = 12 and p = 0.7, we have P (X 3) = 1 P (
Stat 3611
Midterm 1, Spring 2014
ID
Name
Instructions:
You have 50 minutes to complete this exam.
Write answers in the space provided below each question. If you need more room, you can
use the back of the page, but clearly indicate where this is done.
Stat 3611 Homework 9, Spring 2014
Due in class on Apr. 25, 2014
1. (a) The mean x =
1
(2.5 + 3.6 + 3.4 + 4.3 + 2.9 + 2.5 + 3.4 + 4.1 + 2.8 + 3.7 + 3.4)
11
= 3.327.
(b) If we sort these numbers in increasing order, we get 2.5 2.5 2.8 2.9 3.4 3.4 3.4 3.6 3.
Stat 3611 Homework 5, Spring 2014
Due in class on Mar. 05, 2014
1. (a) We can select x oranges from 3, y apples from 2, and 4 x y bananas from 3 in
3 2
3
ways. A random selection of 4 pieces of fruit can be made in 8 ways.
x y 4xy
4
Therefore,
f (x, y) =
Stat 3611 Homework 3, Spring 2014
Due in class on Feb. 19, 2014
1. (a) Sum of the probabilities exceeds 1.
(b) Sum of the probabilities is less than 1.
(c) A negative probability (-0.25).
(d) Probability of both a heart and a black card is zero.
2. Consid
Stat 3611 Homework 8, Spring 2014
Due in class on Apr. 14, 2014
1. P (X > 2.5|X 4) =
P (2.5<X4)
P (X4)
=
42.5
41
= 1.
2
2. (a) P (Z 1.02) = 0.1539.
(b) P (Z 1.83) = 1 P (Z < 1.83) = 1 0.9664 = 0.0336.
(c) P (2.33 < Z < 0.85) = P (Z < 0.85) P (Z < 2.33) =