Probability concepts assumed known

1. RANDOM VARIABLES.
   Discrete and continuous.
   Probability functions and probability density functions.
   Specification of a distribution by its cumulative distribution function (cdf).
   Particular distributions: binomial, negative binomial, Poisson, exponential, uniform, normal, (simple) gamma, generalized gamma, beta, chi-square, t, F.
   
2. MOMENTS AND GENERATING FUNCTIONS.
   Mean and variance of the common distributions.
   Moment generating function of the common distributions,
   Use of moment generating functions and cumulant generating functions.
   
3. BIVARIATE DISTRIBUTIONS.
   Correlation and covariance.
   Marginal and conditional distributions.
   Independence.
   
4. MULTIVARIATE DISTRIBUTIONS.
   Multinomial distribution.
   Mean and variance of a sum of random variables.
   Use of mgf to find the distribution of a sum of independent random variables.
   
5. CHANGE OF VARIABLE TECHNIQUE.
   In the univariate case, given the probability distribution of $X$ and a function $g$, we find the distribution of $Y$ defined by $Y=g(X)$.