1 P(X) represents the probability of X. 2  P(X = x) refers to the probability that the random variable X is equal to a particular value, denoted by x. 3  As an example, P(X = 1) refers to the probability that the random variable X is equal to 1. A probability distribution obtained by means of observation and experimental methods is referred to as an empirical probability distribution, or a relative frequency distribution based on observation. Example: Let X be the number of movies a high school student watches in a given month. Once standardized, a normally distributed random variable has a mean of zero and a standard deviation of one. The standard normal distribution (Z distribution) is shown in the graph below. As you can see from the notation to the right of the curve, mz = 0 and sz = 1. how to convert from PDF to CDF & vice-versa (using exponential distribution as an example) and how to apply CDF to get probabilties. The distribution has a mean of zero and a standard deviation of one. NORMSINV will return a z score that corresponds to an area under the curve. The area should be between 0 and 1. 1  a) Pick a cell and enter a probability into it (for example 0.975), dont forget to add a label so youll know what you put in this cell. Use this empirical probability distribution to find the expected value for the number of movies a high school student will watch in a month. Convert the percentages to decimals. 17% = 0.17. Use the weighted average formula. So, we can expect the average high school student to watch 2.95 movies per month. For example, 1  X represents the random variable X. 2  P(X) represents the probability of X. 3  P(X = x) refers to the probability that the random variable X is equal to a particular value, denoted by x. 4  As an example, P(X = 1) refers to the probability that the random variable X is equal to 1. The distribution has a mean of 0 (zero) and a standard deviation of one. Use this function in place of a table of standard normal curve areas. 1  a) Pick a cell and enter a z score into it (for example 2), dont forget to add a label so youll know what you put in this cell. That is, RAND() generates random probabilities. Therefore, you can use the NORM.INV function to calculate a random number from a normal distribution, using this formula in Excel 2007 and above... =NORM.INV(RAND(), mean, standard_dev). ...and this formula in Excel 2003... Learn How to Calculate the Mean of a Standard Normal Distribution. To see how a random variable is standardized, imagine you have a random variable, x, that is normally distributed with a mean of 20 and a standard deviation of 10.
http://stattrek.com/probability-distributions/probability-distribution.aspx http://hotmath.com/hotmath_help/topics/developing-a-probability-distribution-from-empirical-data.html http://ci.columbia.edu/ci/premba_test/c0331/s6/s6_4.html http://www.youtube.com/watch?v=_adalwwvP90 http://faculty.washington.edu/gloftus/P317-318/Useful%20examples/ExcelNormalDist.html http://hotmath.com/hotmath_help/topics/developing-a-probability-distribution-from-empirical-data.html http://stattrek.com/probability-distributions/probability-distribution.aspx http://faculty.washington.edu/gloftus/P317-318/Useful%20examples/ExcelNormalDist.html http://www.exceluser.com/formulas/statsnormal.htm http://ci.columbia.edu/ci/premba_test/c0331/s6/s6_4.html
how to convert to a probability distribution