STAT 325  Introduction to Probability Models Spring 2009

 

Exam 3 Preparation

 

Logistical details:

  • Date/time/location
    • Thur May 28 from 6:10-8pm in 02-206
    • Fri May 29 from 8:10-10am in 02-206
    • Let me know your choice by 9am on Thur May 28
    • I will trust everyone not to discuss exam with anyone before he/she takes it
  • Coverage
    • Sections 6.1-6.2, 2.5-2.6, 8.2, 7.2-7.3, 10.1-10.2
    • Handouts 18-25
    • HW 18-24
    • But also fundamental ideas from earlier

§         Basics of probability, conditional probability, random variables, expected values

  • Open book, notes, handouts, assignments, solutions
    • You may use anything that I have provided or that you have produced yourself
  • Bring calculator, normal probability table

 

Advice for preparing:

  • Organize your notes
    • Helpful to have well-organized notes during exam
    • Very effective way to study regardless
  • Make use of online resources
    • Handouts, HWs, HW solutions, previous exam solutions
  • Review key ideas, definitions, results from handouts
  • Re-work questions from handouts, assignments
    • Without looking at answers first
  • Work on odd-numbered exercises from text
    • Check answers in back
  • Don’t study less because it’s open book/notes
    • Might refer to book, notes less than you expect
  • Ask questions
    • In class, in office hours

 

Advice during exam:

  • Show method of solution
    • Use clear notation
    • State any assumptions
    • Indicate what rules you are using
    • Be on lookout for simplest way to solve problem
  • Read carefully
    • Answer what is asked for
    • Make use of information provided
  • Be cognizant of time constraint
    • Don’t spend too long on a question
    • Make note of (tentative) point allocations

 

Outline of key ideas (since last exam):

  • Continuous probability distributions
    • Exponential
      • Pdf, cdf, expected value, variance
      • Memoryless property
      • Distribution of sample minimum
    • Normal (Gaussian)
      • Pdf, cdf, expected value, variance
      • Standard normal, z-score, f(z), F(z)
      • Probability calculations, percentile calculations
      • Two types of errors
      • Linear combinations
  • Sampling distributions
    • Basic definitions
      • Random sample, i.i.d.
      • Statistic, sampling distribution
    • Exact calculation
    • Effect of sample size
    • Central Limit Theorem (CLT) for sample mean
      • Derivation of mean, variance for sample mean
      • CLT for normally distributed population
      • CLT for any population distribution
      • Probability calculations
      • Sample size calculations. effects
  • Poisson process
    • Definition, properties
    • Poisson calculations
    • Inter-arrival times
      • Relationship with exponential distribution
      • Calculations, expected value, variance
    • Waiting times for multiple occurrences
      • Relationship with Erlang distribution
      • Calculations, expected value, variance
  • Reliability
    • Definition of reliability function
      • Relationship with cdf
    • Derivation for parallel, series system arrangements
    • Hazard rate
      • Definition
      • Interpretation of increasing, decreasing, constant hazard rates
      • Relationship with reliability function; pdf, cdf of lifetime
  • “Choosing the Best”
    • Problem statement
    • Solution for small samples
    • General solution
    • Asymptotic approximate solution