CS 533 / EE 581 Sample Mid-Term Exam 2

All five problems count equally. In the mathematical problems, show all your work, and do not spend too much time simplifying your answers.

1. For the exponential distribution f(x) = 4e^-4x,

a) calculate P(x > 2).

b) Find the mean and the median of this distribution. (Show appropriate calculations.)

2. a) Based on the data n = 30, X-bar = 47, and s = 2, perform a hypothesis test of μ = 45 vs. μ > 45 with α = 0.05.

b) α is the probablility of a Type I error. What does it it mean that we use α = 0.05? (Don’t explain how to do the calculations; explain what it means that the test is performed with α = 0.05.)

3. a) What is a benchmark program? (Give a definition.)

b) Discuss the shortcomings of the classic benchmark programs, such as Whetstone, Dhrystone, and describe how these shortcomings have been overcome in modern benchmark suites, such as SPEC and TPC.

c) MIPS (Millions of Instructions Per Second) is a common measure of computational speed. Discuss common criticisms of MIPS as a measure.

4. In a simulation program, what information is kept on the event calendar? Explain how the event calendar controls the flow of execution in the running of the simulation program.

5. Find the state probabilities for the queueing system M/M/1/2/2 (a single server queue with capacity 2 and population size 2) by constructing the state transition diagram and solving for the state probablities.