This test is 120 minutes. There are 38 questions, each worth 2.5 points, and a \free" 39th question, worth 5 points (total = 100). In additon, later on, we will add 4 points to everyone’s score (up to a max of 100). But in exchange, you will not be allowed to whine about (and we will not consider) any grade scoring issues unless they involve more than 4 points. Let’s get some additional a
...[Show More]
This test is 120 minutes. There are 38 questions, each worth 2.5 points, and a \free"
39th question, worth 5 points (total = 100).
In additon, later on, we will add 4 points to everyone’s score (up to a max of 100).
But in exchange, you will not be allowed to whine about (and we will not consider) any
grade scoring issues unless they involve more than 4 points.
Let’s get some additional awyer stuff out of the way. . .
You’re allowed the following items:
• Pencil / pen and scratch paper.
• A reasonable calculator.
• Two cheat sheets (4 sides total).
• Normal, t, and χ2 tables. (I will supply these.)
But note that
• You are not allowed to use Arena, even though I’m asking questions about it.
• This test requires some sort of proctor.
• If you encounter a ProctorTrack issue, contact us immediately (but don’t get an
ulcer over it).
Good luck! I want you to make this test sorry that it ever tried to mess around with you!!!
1. Suppose X and Y are continuous random variables with joint p.d.f. f(x; y) =
cxy2; 0 ≤ x ≤ 2; 0 ≤ y ≤ 1, for some appropriate constant c. Find E[2X - 1].
2. Suppose X and Y are discrete random variables with the following joint p.m.f.
Thus, the answer is (d). 2
3. If X and Y are independent Exp(λ = 1) random variables, find Cov(-3X; 4Y - 2).
4. Joey’s Lightbulb Company sells bulbs that have Exp(λ = 1=year) lifetimes. Suppose I just bought 100 lightbulbs from Joey. What is the approximate probability
that the average of the 100 bulb lifetimes will be at most 1.1 years?
has mean µ and variance σ2, then the Central Limit
Theorem implies that
0:8413. So the answer is (b). 2
5. TRUE or FALSE? In Arena, it is not possible use a single DECIDE module to
randomly route customers to one of three or more destinations.
6. TRUE or FALSE? In Arena, you can use the expression EXPO(3) to generate
exponential interarrival times having a mean of 3.
7. TRUE or FALSE? In Arena, an alternative expression to generate exponential
interarrival times having a mean of 3
5
This is the Inverse Transform Method to generate an observation coming from Exp(λ = 3), which has a mean of 1=3. 2
8. TRUE or FALSE? In Arena, it is possible to set the maximum capacity of a queue
from within a QUEUE block found in the Blocks template.
Solution: TRUE. In fact, it’s pretty much the only way. 2
9. What is the variance of the random variable given in the Arena expression
Solution: In Arena, NORM(x; y) corresponds to a normal random variate with
a mean of x and a standard deviation of y. So the variance in question is
10. TRUE or FALSE? In Arena, it is possible to grab more than one resource at a
time in a PROCESS module.
11. TRUE or FALSE? In Arena, it is possible to change the priority in which entities
get processed by a resource.
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