Make in Excel three tables size 50X100,250X100,1000X100 with Bernoulli distribut

Question

Make in Excel three tables size 50X100,250X100,1000X100 with Bernoulli distributed random numbers for p(1)=1/5. Use the generated tables for calculating new column of random numbers equal to the number of the position where 1 appears for the first time in the first 100 columns. Random numbers in this column will have Geometric distribution. Find population probability distribution functions, mean, variances and standard deviations and compare it with sample frequency distribution functions, averages, sample estimation of variances and standard deviations for each table. Draw the graphs.

Explanation / Answer

I always use the RAND function but here are the instructions for the random number generator: Number of Variables Enter the number of columns of values you want in the output table. If you do not enter a number, Microsoft Excel fills all columns in the output range you specify. Number of Random Numbers Enter the number of data points you want to see. Each data point appears in a row of the output table. If you do not enter a number, Excel fills all rows in the output range you specify. Distribution Click the distribution method you want to use to create random values. Uniform Characterized by lower and upper bounds. Variables are drawn with equal probability from all values in the range. A common application uses a uniform distribution in the range 0...1. Normal Characterized by a mean and a standard deviation. A common application uses a mean of 0 and a standard deviation of 1 for the standard normal distribution. Bernoulli Characterized by a probability of success (p value) on a given trial. Bernoulli random variables have the value 0 or 1. For example, you can draw a uniform random variable in the range 0...1. If the variable is less than or equal to the probability of success, the Bernoulli random variable is assigned the value 1; otherwise, it is assigned the value 0. Binomial Characterized by a probability of success (p value) for a number of trials. For example, you can generate number-of-trials Bernoulli random variables, the sum of which is a binomial random variable. Poisson Characterized by a value lambda, equal to 1/mean. Poisson distribution is often used to characterize the number of events that occur per unit of time— for example, the average rate at which cars arrive at a toll plaza. Patterned Characterized by a lower and upper bound, a step, repetition rate for values, and repetition rate for the sequence. Discrete Characterized by a value and the associated probability range. The range must contain two columns: The left column contains values, and the right column contains probabilities associated with the value in that row. The sum of the probabilities must be 1. Parameters Enter values to characterize the distribution selected. Random Seed Enter an optional value from which to generate random numbers. You can reuse this value later to produce the same random numbers. Output Range Enter the reference for the upper-left cell of the output table. Excel automatically determines the size of the output area and displays a message if the output table will replace existing data. New Worksheet Ply Click to insert a new worksheet in the current workbook and paste the results starting at cell A1 of the new worksheet. To name the new worksheet, type a name in the box. New Workbook Click to create a new workbook and paste the results on a new worksheet in the new workbook

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