ISyE 6644 | Fall 2020 | Test #2 SolutionsThis test is 120 minutes. There are 38 questions, each worth 2.5 points, and a \free" 39th question, worth 5 points (total = 100). In addiiton, 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 tha
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ISyE 6644 | Fall 2020 | Test #2 Solutions
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 addiiton, 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.)
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) =
First, we need to find c, so we set:
Thus, E[2X + 1] = 2E[X] + 1 = 11=3. So the answer is (d). 2
2. Suppose X and Y are discrete random variables with the following joint p.m.f.
Thus, the answer is (e). 2
3. If X and Y are independent Nor(0; 1) random variables, find Cov(2X; -3Y + 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 least 1.1 years?
f Xi ∼Exp(1) has mean µ and variance σ2, then the Central Limit
Theorem implies that
And now, several Arena questions. . .
5. ? In Arena, you can use a single DECIDE module to route
customers to that one of four servers having the smallest queue.
2
6. ? In Arena, you can use the expression EXPO(3) to generate
exponential interarrival times having a mean of 1/3.
The mean of an EXPO(3) is 3. 2
7. ? In Arena, an alternative expression to generate exponential
interarrival times having a mean of 1/3 is -(1/3)*LN(UNIF(0,1)).
This is the Inverse Transform Method to generate an observation coming from Exp(λ = 3). 2
8. ? In Arena, it is possible to set the maximum capacity of a queue
from within a SEIZE module.
It is only possible to set a maximum queue capacity from
within a QUEUE block found in the Blocks template.
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