MCS 142 Examination 2

• What: Examination on probability and statistical inference: chapters 4-6 and topics covered in class
• When: 9:00-9:50, Monday, April 28
• Where: Olin 318

Topics that exam problems may cover:

• Probability--the study of randomness
  • Probability models
    • The sample space
    • Events
    • Probability
  • Probability rules
  • Random variables
    • Discrete random variables
      • Probability histograms
    • Continuous random variables
      • Probability density functions (pdf's)
  • Means and variances of random variables
    • Mean and variance of a discrete random variable: summation formulas
    • Mean and variance of a continuous random variable with a pdf: integration formulas
    • Properties of expectation and variance
  • The Law of Large Numbers
• Sampling distributions
  • Sampling distributions for counts and proportions
    • Bernoulli trials
    • Binomial probabilities
    • Binomial mean and standard deviation
    • Normal approximation
    • Continuity correction
  • Sampling distribution of a sample mean
    • Mean and standard deviation of the sample mean
    • Sampling distribution of the sample mean
    • The Central Limit Theorem
• Introduction to inference
  • Confidence intervals
    • The notion of a confidence interval
    • Confidence intervals for the population median
    • Confidence intervals for the population mean
  • Statistical hypothesis tests
    • Steps 0-4
      • Assumptions
      • Hypotheses
      • Test statistic
      • P-value
      • Conclusion
    • Tests for a population mean

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 statistical inference.
• Review the handouts on probability and calculus.
• Make sure that you understand the distinction between a sample and a population, and between statistics/estimators and population parameters. Be able to distinguish conceptually and notationally the mean of a sample, the mean of a population, and the mean of the sampling distribution of the mean.
• Review problems of the following sorts:
  • Calculate probabilities of events, given some basic probability values.
  • Given the probability distribution of a discrete random variable, draw the probability histogram, compute probabilities of events defined in terms of the r.v., and calculate its mean, variance, and standard deviation.
  • Given the probability density function of a continuous random variable, represent and calculate probabilities as areas under the pdf, and calculate the mean and variance by integration.
  • Find means and variances of sums and linear functions of random variables.
  • State the basic assumptions of the "binomial setting," the Bernoulli trials process, and judge whether this model applies in a given application. Compute simple binomial probabilities: P(X = k) = n!/(k!(n-k)!)p^k(1-p)^n-k, and calculate normal approximations when appropriate.
  • Calculate normal probabilities and use normal approximations.
  • Find confidence intervals for population means.
  • Formulate and carry out a statistical test of hypotheses about a population mean.