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# Random Variables

### Review of random variables and standardizing data.

Random Variable A variable that represents the outcome of a probability experiment.
Binomial Random Variable A variable that represents the number of successes in a set amount of trials.
Binomial Distribution A probability distribution with only success or fail outcomes. The random variable represents the number of successes. The probability is found by multiplying the probabilities of each success by the probability of each failure and by the permutations.
Binomial Distribution Probability Formula p(success)^#successes * p(# failures)^#failures * n!/s!f! For all successes p(success)^#trials For all failures p(failure)^#trials
Probability Distribution Table Can be made from a frequency table by dividing each frequency by the sum of the frequencies. The total probability values should be 1.
How would you find P(x = 1 or 4) from a probability distribution? Find x = 1 and x = 4 on the table. The decimal/fraction below each is the probability. Add them together.
How would you find P(x = 1 and 4) from a probability distribution? You can't, in a probability distribution table each separate row or column is mutually exclusive.
Empirical rule In normally distributed data, about 68% of the data is within one standard deviation of the mean, 95% of the data is within two standard deviations of the mean, and 99.7% of the data is within three standard deviations of the mean. expected value
Normal distribution Bell-shaped distribution, centered on the mean
Percentile The nth percentile is the value (or score) below which n percent of the data may be found
Percentile rank The percentage of data that fall below a particular value Example if you are in the 95 percentile, you are above 95% of the rest of the data
Raw Score an original data value, our random variable value
Standard normal curve probability distribution with a mean of 0, a standard deviation of 1, and the area under the curve is 1
Standard score z-score z = (x - mean)/standard deviation
Uniform probability distribution distribution in which all values of a random variable are equally likely to occur, just find the area to find your probability
z-score the number of standard deviations that a data value is from the mean
68-95-99.7 Rule Describes the percentage of data within 1, 2, and 3 standard deviations of the mean.
Mu the mean of a normal distribution
Sigma the standard deviation of a normal distribution
Created by: sgulbis