Types of Distributions
A random variable is a numerical measurement of the outcome of a random phenomenon. It takes on values determined by chance. As with ordinary variables, random variables can be discrete (taking separate values) or continuous (taking values in an interval)
A probability distribution specifies probabilities for the possible values of a random variable. Probability distributions have summary measures of the center and the variability, most notably the mean m and standard deviation s. The mean (also called expected value) for a discrete random variable is
The normal distribution is the probability distribution of a continuous random variable that has a symmetric bell-shaped graph specified by the parameters m (the mean) and sigma (the standard deviation). For z = 1, 2, and 3, the probability of falling within z standard deviations of the mean are 68%,95%, and almost 100%, for any given value of m and sigma
sigma :: Standard deviation of the random variable, probability or population distribution
sigma square :::Variance of the random variable, probability or population distribution
p, 1 - p :: Probabilities of the two possible outcomes (e.g., successor failure) of a binary random variable, and the probability of success in a binomial distribution
generally, the area under the normal distribution between two points a and b gives the probability of falling in this interval
The binomial distribution is the probability distribution of the discrete random variable that measures the number of successes X in n independent trials, with probability p of a success on a given trial. It has probabilities