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 random variable a variable whose values are determined by chance discrete variable discrete variables have values that can be counted continuous variables continuous variables can assume all values in the interval between two given numbers discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values requirements of a probability distribution the sum of the probabilities of all values in the sample space must = 1 the probability of each event must be between or equal to 0 and 1 how do you find the mean for a probability distribution? multiply each possible outcome by it's probability and then find the sum of the products formula for the variance of a probability distribution sum of[X^2*P(X)]-(square of the mean) how do you obtain the standard deviation? square the variance can the standard deviation or variance be negative? no requirements of a binomial experiment 1)trials can only have to outcomes or outcomes that can be reduced to two outcomes 2)There must be a fixed number of trials 3) outcomes must be independent 4)the probability of success must remain the same for each trial binomial probability formula [(n!/(n-X)!X!]*("p" to the power of "x")*[q to the power of (n-x)] p= numerical probability of a success q= numerical probability of failure n= number of trials X= number of successes in trials how do you find the mean of a binomial distribution? n*p p= numerical probability of a success n= number of trials how do you find the variance of a binomial distribution? n*p*q p= numerical probability of a success q= numerical probability of failure n= number of trials How do you find the standard deviation of a binomial distribution? take the square root of (n*p*q) p= numerical probability of a success q= numerical probability of failure n= number of trials