TOPICS FOR IN-CLASS TEST 2, ON CHAPTERS 5, 6 AND 7.1, 7.2, 7.4
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(I) Ch.4 definitions and sources of probability densities: uniform, exponential,
gamma, beta, normal, Weibull; and some others like Pareto
(II) Univariate Change of Variable, plus Probability Integral Theorem that
F_X(X) ~ Unif(0,1) for continuous r.v., which means that
F_X^{01}(U) ~ f_X
(III) Relations among univariate Densities via transformation
(IV) Gamma Function, Beta Integral, Moments of Univariate r.v.'s
(V) DeMoivre-Laplace Limit Theorem: Normal Approximation for Binom(n,p), n large
(VI) Hazard function, hazard rate
(VII) Joint prob mass functions -- discrete case
Joint density functions -- continuous case
Marginal probability distributions (mass function, repectively density function)
INDEPENDENCE OF RANDOM VARIABLES
(VIII) Multivariate Changes of Variables
(IX) Probability calculations, expectations of functions of (multiple) random variables
(X) Expectations and Variances of Sums, Covariance and Correlation
(XI) Convolution and Distributions of Sums of Special Kinds of Independent Random Variables:
Binomial(n,p) with common p
NegBin(r,p) with common p
Poisson(lambda) [different lambda's allowed]
Gamma(a,b) with common b
Normal(mu, sigma^2) [different mu's, sig's allowed]