Download 16 Questions on Engineering Problem Solving II - Exam 2 | EE 300 and more Exams Electrical and Electronics Engineering in PDF only on Docsity!
EE 300, Fall 2009, Exam 2 (take home)
Due 3 December 2009
Page 1/
Name: __________________________________________
First, please sign the statement below, indicating your agreement. You must sign this
statement to receive credit for the exam.
I agree that in return for the trust that has been placed in me by allowing me to
take this exam outside of normal class time, that I have maintained the highest
ethical standards. I have not communicated in any way with anyone other than
the course instructor about the content of this test, nor solutions to any of its
problems, nor have I copied from anyone. I have followed the rules below. On my
honor, the work presented is my own.
Signature: __________________________________________ Date: ______________
You may use calculators, pens and pencils, books, MATLAB, EXCEL, and your brain.
If you use MATLAB or EXCEL, you should include printouts of this work.
You may NOT work with anyone else on this exam. You may NOT post questions nor
receive answers regarding this exam via email, discussion boards, nor forums of any
kind. Do not discuss this test with anyone until both of you have handed-in your papers.
This is a test of what you know.
You may attach extra paper to show supporting work for each problem as needed.
Clearly indicate which problem the work is for. To receive credit for your solutions,
answers must be clearly indicated, and supporting work must be shown.
This exam is to be turned in on paper, at the start of class on the date shown above.
Good Luck!
After you have finished the exam, please answer the following questions. They will
NOT affect your grade.
What grade do you think you made on this exam: ________
How difficult is this exam? (10 = way too hard, 0 = way too easy): ________
Comments:
Name: __________________________________________
1a. [5 points] You are given an unfair coin, with a 75% probability of heads. What is the
probability of getting less than 2 heads in 8 tosses?
1b. [5 points] How unfair does a coin have to be (i.e. what does P(heads) have to be) for
there to be a 50% chance of having no heads in 8 tosses?
Name: __________________________________________
- [20 points total] A survey was made of all of the cars in what we laughably call the
BEC parking lot, with the following results:
- 1/2 of the cars are Hondas,
- 1/4 of the cars are Fords, and
- The rest are some other make.
- 1/3 of the cars are Red,
- 1/6 of the cars are Blue, and
- The rest are some other color.
- 1/3 of the Fords are Red.
- 1/3 of the Fords are some other color than Red or Blue.
- 1/12 of the cars are Blue Hondas.
- 1/2 of the Hondas are some other color than Red or Blue.
You are going to pick a car from the lot, "at random."
a. [5 points] What is the probability of selecting a Red Honda?
b. [5 points] Is the probability of selecting a Red car independent of selecting a Ford?
c. [5 points] Is the probability of selecting a Red car independent of selecting a Honda?
d. [5 points] What is the probability of selecting a Red car that is neither a Ford nor a
Honda?
Name: __________________________________________
- [5 points] A new kind of car has 3 tires. If one or more of the tires has a flat, the car
cannot drive. The probability of each tire having a flat is independent, and is 0.05. What
is the probability of the car being able to drive?
- [5 points] As a publicity stunt, an aging rock star is hanging over the grand canyon by
a 3-link chain. The probability of a failure for each link in the chain is independent, and
is 0.05. What is the probability of the aging rock star surviving his publicity stunt?
Name: __________________________________________
- [15 points] Sketch the following probability density function (pdf), also known as
"probability function" or "little-f". Write an equation and sketch the corresponding
Cumulative Distribution Function (CDF), also known as "distribution function" or "big-
F". Is this random variable discrete or continuous?
f Y
( y ) =
0.4 y = " 1
0.1 y = 1
0.3 y = 2
0.2 y = 4
0 otherwise
Name: __________________________________________
- [5 points, 1 point each] A continuous random variable, V is uniformly distributed
between 3 and 7. Find the following probabilities:
a) P( V ≤ 4 )
b) P( V < 4 )
c) P( 1 < V ≤ 6 )
d) P( 5 < V )
e) P( V ≤ 5 OR 6 < V )
Name: __________________________________________
- [5 points] A random variable, B, is binomially distributed, with n=7 and p=0.3. Find
the following probabilities.
a) P( B ≤ 2 )
b) P( B < 2 )
c) P( 6 ≤ B )
Name: __________________________________________
- [5 points] A random variable, C, is normally distributed, with μ=10 and σ=0.5. Find
the following probabilities.
a) P( C ≤ 9 )
b) P( 9.1 < C ≤ 11.1 )
c) P( C ≤ 8.8 OR 10.8 < C )
Name: __________________________________________
- [15 points total] For a sample data set with sample size=10, sample average=96.
sample standard deviation=12.7:
[5 points] Compute a point estimate of the population mean
[10 points] Compute a 95 % confidence interval for the population mean.
Name: __________________________________________
- [10 points] For a sample data set with sample size=1000, sample average=129.
sample standard deviation=64.8, compute a 99 % confidence interval for the population
mean.
Name: __________________________________________
15 c. [5 points] To what confidence level is this production run longer than a normal
production run?
Name: __________________________________________
- [10 points, 2 points each] Given the following set of sampled data:
X Y
5 1
6 2
4 1
8 3
6 1
3 1
5 2
7 3
Compute the mean and standard deviation in X, and in Y, and the correlation between X
and Y.
mean (X) = _______________
std dev (X) = _______________
mean (Y) = _______________
std dev (Y) = _______________
corr (X,Y) = _______________
