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STA 2302PROBABILITY AND STATISTICS IV (45 Contact Hours)a)Course Purposeb)Course Objectivesi.State the central limit theorem, and apply it.ii.Define the conditional expectation of one random variable given the value of another random variable, and calculate such a quantity.iii.Show how the mean and variance of a random variable can be obtained from expected values of conditional expected values, and apply this.iv.Derive the moment generating function of the sum of a random number of independent, identically distributed random variables (a compound distribution), and use the result to calculate the mean and variance of such a distribution.c)Course DescriptionRandom and mean vectors. Covariance matrix and its properties. Linear combination of random variables. Multivariate normal distribution: definition of non-singular multivariate