Probability and Probability Distributions I & II: Course Outline for Probability and Probability Distributions II (STAT-406)

• Transformation Techniques.
• Derivations of sample mean & variance with their independence.
• Characteristic functions with properties.
• Inversion Theorems for continuous and discrete random variables. 
• Convolution of Distributions. 
• Properties of Cauchy, Laplace, Weibull, Maxwell, Pareto, Rayleigh and Log normal distributions with applications in various fields.
• Order Statistic.
• Distribution of r^th & s^th order Statistics.
• Distribution of median.
• Range. 
• Midrange and quantiles. 
• Central and Non-central t. 
• F and Chi-square distributions. 
• Distribution of Quadratic Forms. 
• Distributions under linear constraints. 
• Truncated Distributions.

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