Simulate a random sample of size N from Y to investigate the strong law of large numbers (SLLN) by plotting the sample averages

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1) Let Y follow a discrete uniform distribution on the set (1, 2, ..., m}.

Simulate a random sample of size N from Y to investigate the strong law of large numbers (SLLN) by plotting the sample averages? = against N, for some values

of in and N. Add a horizontal line for theoretical mean to your plot. What conclusions can you draw from this plot? (5 marks)

2) Let the random variable X have probability density function Generate a random sample of 50000 draws from X, for some values of ß and p, using a random sample of size 50000 from the U(O,1) distribution.

Use your random sample from X to estimate P(X < a), for some a Comment on whether this estimate is consistent with an analytic calculation using the pdf of X. (5 marks)

Choose a set of reasonable values form, N, p, fi, and a which satisfies the given conditions.Write a very brief report consisting of your R code, with appropriate comments, supplemented by your answers to parts (l)—(2) above.[Total 10 marks)

 

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