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EE 300, Fall 2007, Exam 2
16 October 2007
Page 1 / 8
Name: __________________________________________
Rules:
You may use calculators, pens, pencils, books, and your brain.
You may NOT work with anyone else on this exam. Do not discuss this test with anyone
until both of you have handed-in your papers. This is a test of what you know.
Show Your Work. Just writing the answer without supporting work or an
explanation is not enough! Attach extra paper if needed. Clearly label all work done
outside of the indicated areas.
Clearly indicate your final answers.
The test is due at the end of the class, at 12:15pm.
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: __________________________________________
- [35 points total] For the following function,
- [2 points] Identify if this is a discrete or continuous random variable
- [3 points] Identify if it is a CDF, or pdf.
- [5 points] Compute the constant, A, to make it a valid CDF or pdf.
- [5 points] If this function is a pdf, determine an equation for the corresponding
CDF. If this function is a pdf, determine an equation for the corresponding CDF.
- [10 points] Sketch the pdf and CDF functions.
- [10 points, as listed below] Find the indicated probabilities (on the following
page).
g ( x ) =
A 1 " ( x " 3 )
2
[ ]
2 # x # 4
0 otherwise
Name: __________________________________________
- [15 points total] For the following CDF (Distribution function),
- [10 points, 5 points each] Sketch the pdf and CDF functions.
- [5 points, as listed below] Find the indicated probabilities, below.
F
X
( x ) =
0 x < 1
4 x " 4 1 # x < 1.
1
4
x +
1
8
1.1 # x < 1 , 9
4 x " 7 1.9 # x < 2
1 2 # x
[2 points] Find P(1.05 < X < 1.95).
[3 points] Find P(0.5 < X < 1.5).
Name: __________________________________________
- [10 points total] A web server is connected to the Internet. The number of web page
requests waiting at any point in time is distributed by a Poisson distribution, with an
average of 5 pending requests waiting in line. The manufacturer of the server is a
cheapskate, and only builds enough buffer space to hold up to 8 pending requests. When
any more requests arrive they are thrown away and thus ignored.
[5 points] What is the probability that a request will be lost by this server?
[5 points] How long does the buffer have to be to guarantee that 99.9% of the requests get
processed?
Name: __________________________________________
- [15 points total] A factory produces I-beams. The length of the I-beams as they come
off of the production line is normally distributed, with a mean of 24 feet (or 288 inches),
and a standard deviation of 2 inches. A beam is considered defective if it is more than 3
inches different from the required 24 feet.
[5 points] What is the probability that a beam is defective?
[5 points] What is the probability that a beam will be longer than 24 feet and 1 inch?
[5 points] What is the probability that a beam will be longer than 24 feet and 1 inch,
given that it has been tested and is not defective?
Name: __________________________________________
- [10 points total] The weight of trucks on a highway is normally distributed, with an
average weight of 70,000 pounds. The Department of Transportation considers a truck
over weight if it weighs more than 80,000 pounds on this highway. Studies have shown
that 10% of the trucks are overweight.
[3 points] What is the variance of the weight of the trucks? What is the standard
deviation of this weight?
[3 points] If the trucking companies want to make sure that only 1% of the trucks are
overweight, but they cannot easily change the variance of the truck weights, what new
average weight do they need to set for the trucks to achieve this goal?
[3 points] If the trucking companies still want to make sure that only 1% of the trucks are
overweight, but this time they want to have an average weight of 75,000 pounds, what
standard deviation of the weight do they need to achieve?
[1 point] Free, because you're done. Smile!
