MCS 142 Examination 2

• What: Examination on chapters 3-4 and topics covered in class
• When: 11:30-12:20, Friday, October 27, 2006
• Where: Olin 317

Old Exam 2
Caution: Do not assume that your Exam 2 will exactly parallel this one.

Answers

Topics that may be covered on the exam include the following.

• Collecting/gathering data
  • Design of experiments
    • Completely randomized design
    • Block designs
    • Response variables, factors, levels, experimental units/subjects
    • The three principles of experimental design
    • Double-blind design
    • Placebo effect
  • Sampling design
    • Probability sample
    • Simple random sample (SRS)
    • Other: voluntary response, convenience, stratified, multistage
• Toward statistical inference
  • Populations and parameters
  • Samples and statistics
  • Sampling distribution of a statistic
  • Bias and variability
• Probability--the study of randomness
  • Probability models
    • Sample space
    • The events
    • Their probabilities
  • Probability rules and assigning probabilities (see p. 323)
    • P(A) is nonnegative; P(S) = 1;
      P(A or B) = P(A) + P(B) if A and B are disjoint;
      P(A or B) = P(A) + P(B) - P(A and B) in general;
      P(not A) = P(A^c) = 1 - P(A);
      P(A and B) = P(A)P(B) if A and B are independent;
      P(A and B) = P(A)P(B|A) in general.
    • Conditional probability
  • Random variables (r.v.)
    • Discrete random variables
    • Probability functions for discrete random variables
    • Continuous random variables
    • Probability density functions (pdf) for continuous random variables
  • Mean or expected value or expectation of a r.v. (or its distribution)
    • Discrete r.v.
    • Continuous r.v. with a pdf
  • Variance and standard deviation of a r.v. (or its distribution)
    • Discrete r.v.
    • Continuous r.v. with a pdf
  • Properties of means (expected values) and variances (see p. 305)
    • Constant multiples of r.v.s
    • Sums and differences of r.v.s
  • The Law of Large Numbers (LLN)

Suggested study and preparation:

• Review the summaries at end of each section of the text. Make sure that you know and understand the terminology of probability and statistics.
• Be prepared to demonstrate statistical and probabilistic thinking in context.
• Review problems introduced in class and on the homework, as well as supplemental exercises.
• Be prepared to identify parameters, statistics, kinds of samples, etc.
• Be prepared to draw up or critique experimental designs.
  Review the three principles of good experimental design.
• Be prepared to classify and critique sampling designs.
• Be able to use Table A (standard normal probabilities) and Table B (random digits).
• Be able to identify legitimate assignments of probabilities to outcomes.
• Be prepared to calculate probabilities, means, variances, and standard deviations for discrete random variables.
• Be prepared to do simple calculus calculations (or set-ups) to find probabilities, means, variances, and standard deviations for a continuous random variable, given its probability density function.
• Be prepared to give the Law of Large Numbers interpretations of means and probabilities.