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# Set number of observations in your data set to 10 and number of samples to 500

INSTRUCTIONS TO CANDIDATES

a. (5 points) Set number of observations in your data set to 10 and number of samples to 500.

b. (5 points) Let X be a discrete RV and suppose in the population it can take values 10, 20, 30, 40, and 50 with equal probabilities i.e. P(X = 10) = P(X = 20) = P(X = 30) = P(X = 40) 40) P(X 50)=.2 Get a random sample of size 10 from the population described. Do it 500 times.

=

c. (5 points) For each sample you get above (500 samples total) calculate the sample mean and sample variance. d. (5 points) How does the distribution of sample mean look like? Draw a histogram. What about the distribution of sample variance? Remember we are looking at the values of sample means and sample variances over 500 samples.

e. (5 points) Follow the same steps above for sample sizes 50, 100, 500, and number of samples 50,100, 500. Interpret your results. Conceptually, sample variance and variance of sample mean are two different things. Make sure you understand this. What happens to sample variance as sample size gets larger? What happens to the variance of sample mean as sample size gets larger? Comment.

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