Exam III info:

What to bring:

  pencil and eraser
  no calculators
  copy of Tables 1 and 2 (normal tables) will be provided
  copy of Table 3 (MGF table) will be provided
  formulas for large-sample CI for mean mu (and sample size calculation) will be provided.

Calculus:  Know how to

  Integrate/differentiate polynomials
  Integrate/differentiate exponentials
  Differentiate natural log (ln)
  
Sections/Topics covered:

  Chapter 6, section 6.2
  Chapter 7, sections 7.2 and 7.3
  Chapter 8, sections 8.1-8.3
  Chapter 11, sections 11.1-11.3 and 11.5
  Properties of Sample Average - book and class notes  
  Large-Sample CI for mu and sample size calculation (not in book)

HW's covered:  HW's 10-14 and HW 15, problems 1-4

The following list of topics is not guaranteed
to be exhaustive but is a good place to start for reviewing:

Chapter 6:  Know the following

  How to compute probability density function of Y = H(X), where H is any function; X is continuous RV
  How to compute cumulative density function of Y = H(X), H any function; X continuous RV.

Chapter 7:  Know the following

  How to do normal calculations (7.2)
  Properties of exponential distribution (7.3):
    probability density function of exponential - provided by Table 3
    mean, variance - provided by Table 3
  How to do problems requiring exponential distribution (7.3)
  Relation to Poisson Process (7.3)

Chapter 8:  Know the following:

  How to work with/use following functions associated with bivariate RV's (8.1):
    joint probability mass function (PMF)
    joint probability density function (PDF)
    marginal probability mass function
      how to get from joint PMF
    marginal probability density function
      how to get from joint PDF
    joint cumulative distribution function (CDF)
      how to get joint CDF from joint PDF
      how to get joint PDF from joint CDF
    computing expectation of functions of two continuous RV's, E[h(Y,X)]

  Definition and properties of independent RV's (8.2):
    How fact that independent RV's simplifies probability and expectation computations
    How to determine if two RV's are independent
    How to determine joint pdf of two independent RV's from their respective pdf's
    Know that functions of independent RV's are independent
 
  Know definition and properties of conditional distributions (8.3):
    How to compute conditional pmf from joint pmf
    How to compute conditional pdf from joint pdf
    How to compute E[X|Y=y]

Chapter 11:  Know the following:

    Definition and computation of moment-generating functions (MGF's) (11.1)
    How to use mgf's to determine distribution of sums of independent RV's, i.e.,
      distribution of Y = X_1 + X_2 + ... + X_n, X_i's independent  (11.2)
    Know to use Chebychev's inequality - both forms given in class (11.3)
    Know CLT (Central Limit Theorem) (11.5)
    Know properties of sample mean (sample avg) given in class:
      mu_avg = mu
      sigma_avg = sigma/sqrt(n)
      avg of normal RV's is exactly normal for all n
      CLT: avg of non-noromal RV's is approx. normal for n "large enough," say n >= 20.

Statistical Application: class notes and handouts; first page of formula sheet
    Know how to compute large-sample 100*(1-alpha)% confidence interval for mu
    Know how to determine sample size to guarantee avg within epsilon of mu with
      probability 100*(1-alpha)%
    Know properties of confidence intervals:
      how to interpret
      confidence level = success rate
      1 - confidence level = failure rate = 100*alpha%