Unit Objectives By the end of this unit students should be able to: · Find and use cumulative distribution functions for both discrete and continuous distributions. · Solve problems using the geometric distribution and negative binomial distribution · Find and use probability generating functions and their properties · Solve problems involving linear combinations of random variables, their expectations and variances · Find and use unbiased estimators and estimates · Know and use the Central Limit Theorem · Find confidence intervals for the mean of a normal population · Carry out one and two tailed hypothesis tests. · Identify and find probabilities of Type I and Type II errors · Calculate the covariance and (population and sample) product moment correlation coefficient for bivariate data · Interpret r and R in terms of correlation · Use the t statistic to test the null hypothesis ρ = 0 · Know the facts that the regression of X on Y and Y on X are linear · Calculate least-squares estimates of these regression lines · Use regression lines to make predictions
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