# hw1 - f ( x ) = 4 5 p x 5 P 3 e-( x/ 5) 4 , &amp;amp;lt; x...

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STAT 428 Spring 2010 Homework #1 Jan 27 Homework 1 Due in class on Wednesday, Feb 3. 1. Use the naive Monte Carlo method to estimate E ( X 6 ), where X has a normal distribution with mean 3 and variance 4. Describe your algorithm and implement it in R. Give your estimate of E ( X 6 ) based on 1000 samples, and estimate the variance of your estimate. Attach your R code. 2. Suppose U Uniform(0,1). Describe how to use the inverse CDF method to generate a sample from the Weibull distribution with the following pdf:
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Unformatted text preview: f ( x ) = 4 5 p x 5 P 3 e-( x/ 5) 4 , &lt; x &lt; . Use the inverse CDF method to generate 1000 samples from the above Weibull distribution in R. Based on this sample, estimate the mean, median, and variance of this distribution. Attach your R code and results. 3. Suppose U Uniform(0,1). Describe how to use the inverse CDF method to generate a sample from a distribution with the following pdf: f ( x ) = b x, x 1 , 2-x, 1 &lt; x 2 ....
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## This note was uploaded on 10/24/2010 for the course STAT 428 taught by Professor Chen during the Spring '08 term at University of Illinois, Urbana Champaign.

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