Statistics 6401: Homework 2

• Read Ch2
• Problems Ch2:  16, 27, 31, 56, 59, 60, 66, 67
• Read Problems Ch2 71, 72 (random number generation)
• Read the Handouts on random number generation.

From jStor find and read the following papers.  JSTORE - online statistics and probability articles, available on campus.

• Leemis, Lawrence., Relationships Among Common Univariate Distributions, The American Statistician, Vol. 40, No. 2 (May 1986), pp. 143-146.

• Exercise 1:  Write an R program to implement the linear congruential method for RANDU. Hint: the R code for mod is %%.  Try 7%%5 answer 2. 

• Exercise 2: Using R verify that Gamma(alpha = n/2, 1/2) = Chi-Square(n).  To show this compute the cumulative probabilities for the two distributions using the pgamma and pchisq commands for the same value of x.  Or use qgammand and qchisq.