Sample Means CBD

# Sample Means CBD - DISTRIBUTION OF THE SAMPLE MEAN for a...

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Sample Size n Mean Variance 6 0.5000 0.0417 0.4917 0.0406 Parameters For M Sample Statistics For 1,000 Sample Means E ( M ) V ( M ) DISTRIBUTION OF THE SAMPLE MEAN for a FINITE RANDOM VARIABLE Let X be the finite random variable which can assume only the values 0 or 1, with P ( X = 0) = P ( X = 1) = 0.5. Let M be the finite random variable which gives the sample mean for a sample of size n from X , and let S be the standardization of M . We are eventually interested in the distribution of S for large values of n . Since S can assume n + 1 values, we will treat S as a continuous random variable. Enter an integer between 1 and 30 as a value for n , in Cell C27 , then press F9 . Excel will pick 1,000 random samples, of size n each, from X . The parameters E ( M ) and V ( M ), and the statistics of mean and variance for the set of 1,000 observations of M will all be displayed. The 1,000 observations of M are used to approximate a plot of the p.m.f . of M , and a plot of the p.d.f . of S . Pressing F9 will select a new sample and redisplay all data. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 SAMPLE MEAN sample mean p.m.f. -4 -3 -2 -1 0 1 0.0 0.1 0.2 0.3 0.4 0.5 STANDARDIZED SAMPLE sample mean p.d.f.

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Approximate p.m.f . of M Approximate p.d.f . of S

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