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MATH474 Probablllty 1 Scorezso
Mid-Exam Solution, 2015 Tota
This exam consists of FIVE questions. Answer all of them.
The data and situations portrayed in this test are ﬁctitious, but realistic.
. . - 6
7 Problems (Listed by Chapter)
Chapter 2: Calculate the probability (proportion) of an event
Chapter 4: Derive the expectation given a pdf.
Chybshevs inequality
Chapter 6: Distribution Normal (only one)
Chapter 6: Normal approximation of the binomial dist
MATH 474 Probability and Statistics
Review for Final Exam
Lulu Kang
Fall, 2016
Chapter 1 Probability &
Statistics Concepts
Deterministic Model Deterministic Event
Probability Model Random Event
Population
Sample: the larger the sample is, the closer the s
MATH474 Probability & Statistics
Final Test, Spring 2012
Instructions:
i. This exam consists of EIGHT questions. Answer all of them.
ii. The data and situations portrayed in this test are fictitious, but realistic.
iii. Show all your work to justify your
(d) 1 0.05 0.32 = 0.63 = 63%.
since the second of the three integrals is nonnegative. Now, since |s fi\ > ka
2.71 (a)wherever
0.12 + 0.19
s > p=+ 0.31;
ka or x < p - ka, we have (x - p)2 > k2a2 in both remaining
integrals. It follows that
30
(b) 1 0.07 =
30
C hapter 3 Random Variables and Probability Distributions
C hapter 6 Some Continuous Probability Distributions
74
3
MATH474
Probability & Statistics
2
3.5 (a)
(a) xc =
1/ 30 since 1 = =c(x
4) = 30c.
6.18
+1.3.
T hen z1 = 1.3 and z2 = 1.3. P (X >
1 = +
Expectation E(g(x) =
P
S
g(x)f (x) =
R
S
g(x)f (x)dx
Independent Events A and B are independent if knowing whether A occurred gives no information about whether B occurred. More
formally, A and B (which have nonzero probability) are independent if and onl
MATH 474 Probability & Statistics for Engineers
Lecture Notes
Lulu Kang
Room 105B, Bldg E1, Department of Applied Mathematics
Phone: 312 567 5322, Email: [email protected],
Wed 24 pm or by appointment.
Course Information on Piazza via http:/piazza.com
Lulu K
MATH 474 Homework 1
Due on Sept 6, 2016, Total=30 pts
Homework submission:
1. MATH 474-01 students must submit homework in class except for reasons approved
by the Instructor.
2. MATH 474-02 students must email your homework to the TA Zhuan Cheng
(zcheng9
MATH474 HW 2
Nash Kaminski
3 September 2015
Answers
Question 1
a. nitrogen, potassium, uranium, oxygen
b. copper, sodium, zinc, oxygen
c. copper, zinc
d. copper, uranium, zinc
e. empty set
f. oxygen
Question 2
a. 45 = 1024
b. Three ways to choose a wrong
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MATH474 Probability & Statistics
Sample Mid-Exam
Instructions:
i. This exam consists of FIVE questions. Answer all of them.
ii. The data and situations portrayed in this test are fictitious, but realistic.
iii. This exam is closed book, but you may use 1