Hi: Attached is the question. Thanks so much.
1. Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( XX ) when X has a U [01] distribution. Plot the value of the approximation as the sample size goes from 1 to 10000. Use the Notebook feature in RStudio to create an HTML file for your answer. 2. Simulation of a Polya Urn. Put a = 10 white balls and b = 20 blue balls in an urn. Then randomly draw a ball from the urn and replace it along with another ball of the same color repeat. a) Write an R program to simulate Rn the proportion of white balls in the urn after n draws from the urn for any integer n. b) Plot the histogram of Rn for n = 1000. c) Simulate Rn 10000 times. d) Overlay the histogram with a line graph of the appropriate limiting distribution. Use the Notebook feature in RStudio to create an HTML file for your answer.
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