MA 2631 - Probability II for AS

• Understand and apply continuous probability distributions to appropriate probability situations
• Understand, derive, and use continuous probability density functions, conditional probability density functions, marginal functions, and moment-generating functions
• Understand, derive, and use continuous joint probability functions
• Understand the meaning and relevance of and use measures of dispersion for continuous multi-variable probability distributions
• Understand, calculate, and use covariance
• Understand, calculate, and apply to correlation coefficient appropriate situations
• Perform transformations of continuous random variables
• Form and use linear combination of random variables with respect to calculation of probabilities and moments

• Multivariable calculus
• Discrete random variables

• Continuous probability distributions such as the Gaussian (normal) distribution, Student-t, chi-squared, F, exponential, gamma, beta, etc.
• Continuous probability density functions
• Continuous cumulative density functions
• Continuous moment-generating functions
• Continuous joint probability functions, joint probability density functions, and joint cumulative density functions
• Conditional and marginal distributions and densities
• Moments for the discrete and continuous joint functions considered
• Joint moment-generating functions
• Measures of dispersion for multi-variable probability distributions
• Covariance
• Correlation coefficients
• Transformations of continuous random variables
• Linear combinations of random variables including probabilities and moments