Written by Scott D. Anderson, © 2004
Scott.Anderson@ACM.org
Creative Commons License
This work is licensed under a Creative Commons License.

Exam Two Review

Please bring your own questions to pose: I'd rather spend our time on questions you have than questions I make up.

Topic Reminders

  • Probability and Statistics
    • Moments and Parameters
    • Mean (Expected Value) of a Distribution
    • Mean of a Binomial
    • Mean of a Poisson
    • Variance and Standard Deviation
    • Variance of a Binomial
    • Variance of a Poisson
    • Continuous Distributions
    • Probability Density Functions
    • The Uniform Distribution
    • Triangular Distribution
    • Exponential Distribution
    • The Cumulative Distribution Function (CDF)
    • Integrating the Exponential Distribution
    • The Normal Distribution
    • Gaussian PDF
    • CDF of the Gaussian
    • Standard Units
  • Probability Concepts
    • Hot Hands
    • The Gambler's Fallacy
    • The Law of Large Numbers and Pattern Perception
    • Perceptions of Randomness
  • Simulation Modeling
    • Discrete Event Simulation
    • The M/M/1 Queue
    • Global Heat
    • Cold Falling Rubidium Atoms
    • Grocery store (express lane and regular lane)
    • Bimodal Distributions
    • Attributes
    • Hierarchical Models
    • Fast Food Operation
    • Queuing Models
    • Text boxes
    • Cloning
    • Meters
  • Hypothesis Testing
    • Real differences versus Chance Differences
    • Type I and Type II Errors
    • Two Sample tests: z, t, and bootstrap
    • The Standard Error of the Mean
    • The Central Limit Theorem
    • Student's t
    • Degrees of Freedom
    • One Tail or Two?
    • Power of a Test
  • Confidence Intervals
    • Point Estimates
    • Confidence Interval for the Mean
    • 95 Percent Confidence
    • Bootstrap Confidence Intervals
  • DES Implementation
    • Event Scheduling
    • Priority Queues
    • Linear Queues
    • Heaps as Queues

List of Models

In alphabetical order, they are:

List of Blocks

In order from the menus

  • DE Lib
    • Activity, Delay
    • Activity, Delay (Attributes)
    • Get Attribute
    • Set Attribute
    • Set Priority
    • Batch
    • Unbatch
    • Generator
    • Count Items
    • Information
    • Queue, FIFO
    • Queue, Priority
    • Resource
    • Combine
    • Exit
    • Select DE Input
    • Select DE Output
    • Executive
  • Generic Lib
    • Decision
    • Select Input
    • Select Output
    • Accumulate
    • Holding Tank
    • Wait Time
    • Constant
    • Input Random Number
    • System Variable
    • Add, Subtract, Multiply, Divide
    • Max & Min
    • Equation
    • Mean & Variance
  • Plotter Lib
    • Histogram
    • Plotter, I/O
    • Plotter, Discrete Event
    • Plotter, MultiSim

What test to use?

  • If the samples are small (fewer than 30), and the samples come from Gaussian distributions (how would you know?), and you're using means, use the t-test.
  • If the samples are many (more than 30) and you're using means, use the z-test or the t-test (they're the same).
  • If all else fails, use the bootstrap.

Problems

  1. Estimate (why?) the mean of a negative binomial with 3 successes and P=0.5
  2. Estimate the variance of that population
  3. You've just flipped a fair coin 5 times and gotten 4 heads. Which probability is bigger: getting 3 heads in the next 5 flips or getting 2 in the next 5 flips.
  4. You're tossing a coin with unknown probability of heads. Which is more likely: HT or TH?
  5. What is the probability of a z value falling between 1.5 and 2.5?
  6. If student scores on the GRE are normally distributed with mean 500 and standard deviation 100, what is the probability of getting a score between 600 and 700? Above 700?
  7. What is the probability of getting an exponential random number (mean of 5) larger than the median?
  8. What is the median of an exponential distribution of mean 5?
  9. Test whether the following two samples are significantly different.
    A: 38,74,48,17,47,29,50,78,58,64,58,36
    B: 86,37,76,32,68,49,28,67,48,27,47,39,24
  10. You collect two samples of data. Here are the summary stats. Are they significantly different? What test do you use?
    A: x-bar=35.6, var=12.7, N=42
    B: x-bar=38.3, var=9.8, N=29
  11. You collect two samples of data. Here are the summary stats. Are they significantly different? What test do you use?
    A: x-bar=14.6, var=11.2, N=15
    B: x-bar=19.3, var=35.9, N=18
  12. What is the mean and standard error of the following sample?
    83,74,48,17,47,29,50,72,55,63,58,36
  13. You record the value of the Dow Jones Industrial Average every day for a month. Is the mean value likely to be normally distributed?

Modeling Problems

  1. Create a model in there are 4 checkout lanes. 10 percent of customers buy beer. People who aren't buying beer prefer to go to the lane that has the fewest beer purchasers, because, well, y'know.
  2. Items to be painted arrive on a conveyor belt. They go to the painting room, where the sprayers take about 5 minutes (Gaussian, sd=1) to paint the items. They then go to the drying room. If they took more than 5 minutes to paint, they take 10 minutes to dry (Gaussian, sd=2), but if they took less than 5 minutes to paint, they take 8 minutes to dry (Gaussian, sd=2). What is the average time to complete an item?
  3. Build a model that tests the 0.05 level critical value of the t distribution for 3 degrees of freedom.
  4. Build a model of a round-robin scheduler for a car engine. There are 5 regular tasks, each of which takes an amount of computation time that is triangular: min 2, mode and max=5. There are also "occasional" tasks, that arrive exponentially with mean 200 and take computation time of 25. What is the average waiting time of the regular tasks?