ECE 3800
Test I
S13
Name:__________________________________
Date:___________________________________
Instructions:
The test is 50mins in length starting at 9:30am and ending 10:20am. At the end of the
allotted time promptly turn in your test. You will be given a 5min warning at 10:15am.
This is time to finalize your work.
You are allowed your calculator and you text book. Other materials such as notes or
note cards are not permitted. You may use scrap paper, but make sure you include your
name on any additional work. If you need Integration or Normal Distribution tables one
is provided in the text appendix.
Make sure your work is neat and readable. Box your final answer. Partial credit for your
work will be considered, so attempt all problems. Partial credit is given for work which is
clearly an attempt at a specific question or sub question. Since this is an open book
exam copying book equations yields little to no points.
1
ECE 3800
Test I
S13
1. (20pt) A large bin of capacitors is a mix of capacitances and voltage rating. A
table of the quantities is listed below.
Rating
25v
50v
100v
100 F
25
75
25
Capacitance
470 F
620 F
40
35
20
35
10
35
a. Solve for the marginal probability of picking a 620 F resistor.
b. Solve for the joint probability of picking a 100F and 100v.
c. A 470F capacitor is selected from the bin what is the conditional probability the
voltage rating is 100v?
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ECE 3800
Test I
S13
2. (30pt) An exponential distribution is given the equation:
( )
(
⁄
)
A second distribution is related to x by:
a. Solve for the density function fy(y) and make a sketch of the function.
b. Solve for the mean of fy(y).
c. Solve for the variance of fy(y).
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ECE 3800
Test I
S13
3. (30pt) A random variable X has a density function:
( )
[
( )
]
( )
a. Sketch the density function and solve for the coefficient A.
b. What is the probability X is less than or equal to
?
c. What is the Expected Value of x?
d. Solve for the variance of x?
4
ECE 3800
Test I
S13
4. (20pt )A Gaussian distribution has a mean of 200 and a variance of 65. Round
numbers to the third decimal place. Use the Normal Distribution Table when
directed.
a. Solve for the probability a random variable will be greater than 203.225 and less
than 209.514. Use the Normal Distribution Table.
b. Solve for the probability a random variable is less than 190. Use the Normal
Distribution Table.
c. Solve for the probability a random variable is greater than 215.
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