AC 2303 - AS Lab I: Applications of Probability

• Calculate probabilities of mutually exclusive events
• Calculate probabilities using addition and multiplication rules
• Calculate probabilities using combinations and permutations
• Calculate conditional probabilities
• Use Bayes theorem to calculate probabilities
• Apply probability mass, probability density, and cumulative distribution functions
• Calculate expected value, mode, median, variance, and standard deviation
• Calculate probabilities using probability generating and moment generating functions
• Perform calculations concerning joint probability and probability density functions, and cumulative distribution functions
• Determine conditional and marginal probability and probability density functions, cumulative distribution functions
• Calculate moments for joint, conditional and marginal random variables
• Apply joint moment generating functions
• Calculate variance and standard deviation for conditional and marginal probability distributions
• Calculate joint moments, such as covariance and correlation coefficient

• Combinatorial probability
• Probability rules 
• Conditional probability
• Total probability law and Bayes theorem
• Discrete random variables
• Binomial, Poisson, geometric, and other discrete distributions
• Continuous random variables
• Normal, chi-Square, t-distribution and other continuous distributions
• Mixed random variables
• Marginal distribution
• Moment generating functions
• Measures of central tendency and dispersion

• Application of probabilities of mutually exclusive events
• Applications of probabilities using addition and multiplication rules
• Applications of probabilities using combinations and permutations
• Applications of conditional probabilities
• Applications of Bayes theorem to calculate probabilities
• Probability mass, probability density, and cumulative distribution function applications
• Applications of expected value, mode, median, variance and standard deviation
• Calculate probabilities using probability generating and moment generating functions
• Applications of joint probability and probability density functions and cumulative distribution functions
• Applications of conditional and marginal probability and probability density functions, cumulative distribution functions
• Applications of moments for joint, conditional, and marginal random variables
• Applications of variance and standard deviation for conditional and marginal probability distributions
• Applications of joint moments, such as covariance and correlation coefficient