Quiz 9 1. Give the following properties of a Poisson random variable X; a) What is the proba bilitv mass function (pmf) of rv X? b] What is the expected value of rv x? c] The variance of rv x is equal to... d] The rate ofthe Poisson process is given as... e) At which condition can one use the Poisson probabilities to approximate binomial probability (or approximate Poisson probabilities using binomial probability]? f) Give the moment generating function of rv x. 2. Give the appropriate probabilitv distribution, as well as the corresponding parameter values for each of the following random variables; a) Suppose that random variable x denotes the number of successes in 30 of independent dichotomous trials, where 0.4 [the proba bilitv of a success) is constant in each trial. b] Suppose that random variable X denotes the number of successes obtained in a sample of size 30 without replacement from a population of size 100, containing 00 failures, where each subset of 30 has an equal chance of being chosen. c] Suppose that random variable x denotes the number of successes observed in an interval, where the successes occur at a tempo of 30 per interval. d] Suppose that random variable X denotes the number of failures observed before the 30'\" success is found {which means that there are 29 successes in the first (x+29] trials and a success on the last trial. The probability of success for any trial is given as 0.40