Review Test 1 ST315 Material allowed on the exam 1. A TI calculator 2. Copy of normal table 3. Copy of binomial table (upto n=12) 4. A formula sheet 8.5x11 (one sided) to be attached with the exam. Given a data set , compute the mean , variance, range , median interquartile range. Set theoretic presentation of the sample space S and the events in S(e.g. Exercise 3.12 and 3.14 Three axioms of probability Probability of union of k events Probability of intersection of any two events Probability of intersection of independent events Mutually exclusive events and complementary events. Exercise 3.49 Conditional probability and multiplication rule of probability Rule of total probability (i.e. partition of an event into disjoint parts) Bayes theorem (just statement and proof no problem solving) Exercise 3.64 Find probabilities of different events from the given classification table (exercise 3.109) Chapter 4 Moments of a discrete distribution Binomial distribution its probability mass function, its mean, its variance, parameters, Interpretation of parameters Use of binomial table/ use of a TI calculator to find binomial probabilities. Prove that mean of binomial is np and variance is npq. Poisson distribution its pmf, mean variance parameters, interpretation of parameters. Interpretation of poisson random variable. Approximation of binomial probabilities with poisson probabilities Properties of hypergeometric, geometric and multinomial distributions Exercise 4.7, 4.4, 4.57, 4.48, 4.79, 4.83, Chapter 5 Moments of a continuous distribution Exercise 5.1, 5.6, 5.11, 5.12 Normal distribution, its probability density function and density function Standard normal variate and its properties, the transformation formula Use of normal table Parameters of normal distribution Normal approximation to binomial.