At any other value it is 0. Suppose N is a positive integer and k is any integer. A random variable with range is said to have a binomial distribution if The mean and variance of such a random variable are given by Such a random variable might arise from counting the number of heads in N independent tosses of a coin with probablity p of heads on a single toss. A random variable with range is said to have a geometric distribution if The mean and variance of such a random variable are given by Such a random variable might arise from counting the number of independent tosses of a coin with probility heads until the first head is obtained. A random variable with range is said to have a hypergeometric distribution if The mean and variance of such a random variable are given by Suppose an urn contains N balls, r of which are red and N-r of which are green.
R represents the number of red balls.
A random variable with range is said to have a Poisson distribution if The mean and variance of such a random variable are given by This a little more complicated to explain, and we shall leave this to another time. Derive the formulae for the mean, variance and standard deviation for the discrete uniform distribution, for the binomial distribution, for the geometric distribution and for the Poisson distribution. You will find it helpful to read the proofs of Theorems 3.7, 3.8, and 3.11 in your text. Graph the probability mass function and the distribution function for a random variable with a binomial distribution with expected value of 4 and variance of 2. Graph the probability mass function and the distribution function for a random variable with a binomial distribution with expected value of 3 and variance of 2. 4.