STATISTICS
3N03
TEST #2 -
2001-11-01
Instructions
Aids permitted: any
calculators and one sheet of notes (8.5" x 11", one side
only).
Questions
- Define the following terms:
random
variable, probability density function, expected
value.
- Suppose that ships arrive at a
port at an average rate of 1 per day.
(a) What is the probability that more than two ships will arrive
on the same day? State any assumptions you make.
(b) What is the probability that this will happen on more than two
days next week?
- If the percent yield from Process
A has mean 68 and standard deviation 3, while the percent yield
from Process B has mean 74 and standard deviation 3, and you do
one run of each process, what is the probability that Process A
gives a higher yield than Process B? State any assumptions you
make. [Hint: Find the mean and variance of
YA-YB, where YA
and YB are the yields from Process A and Process
B, respectively, and compute P(YA-YB
> 0). Note that F(1.414) = 0.9214.]
- If a random variable X can take
values 1, 2, 4, 8 with probabilities 0.6, 0.05, 0.05, 0.3,
respectively, plot the probability density function and find the
mode, median, mean, variance and standard deviation of X. If you
know that X is greater than 1, what is the probability that X is
greater than 7?
- You are planning a survey to
study the concentration of arsenic in the buffering material on
the ground underneath public playgrounds build with CCA
pressure-treated wood. The buffering material could be sand, pea
gravel, mulch, or shredded tires. What measurements would you
make? List at least 6 factors that might explain any variability
in your results.