HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 557

Discrete probability distributions A random variable is said to be discrete when it can only take a finite number of values. For example, the number of rainy days in a given location can be considered a discrete random variable because we count them as integer numbers only. Let X represent a discrete random variable, its probability mass function (pmf) is represented by f(x) = P[X=x], i.e., the probability that the random variable X takes the value x. The mass distribution function must satisfy the conditions that f(x) >0, for all x, and ∑ f (x) = 1.0 all x A cumulative distribution function (cdf) is defined as F (x) = P[ X ≤ x] = ∑ f (k) k≤x Next, we will define a number of functions to calculate discrete probability distributions. We suggest that you create a sub-directory, say, HOME\STATS\DFUN (Discrete FUNctions) where we will define the probability mass function and cumulative distribution function for the binomial and Poisson distributions. Binomial distribution The probability mass function of the binomial distribution is given by f (n, p, x) =  n x  ⋅ px ⋅ (1 − p)n−x , x = 0,1,2,..., n where (nx) = C(n,x) is the combination of n elements taken x at a time. The values n and p are the parameters of the distribution. The value n represents the number of repetitions of an experiment or observation that can have one of two outcomes, e.g., success and failure. If the random variable X represents the number of successes in the n repetitions, then p represents the Page 17-4