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Optional Homework Problems The attached page 445 is from the Hays (1973) statistics book. The page contains formulas for the density of F, and the mean and the variance of F. 1. Write a SAS or SPSS program to compute the mean and variance of F for any value of numerator, v,, or denominator, v, degrees of freedom. 2. Write a program for the density function of the random variable F. I am not sure whether SAS or SPSS has a factorial function so check for that first. Note that value of the density function is for a given value of F and numerator, v, or denominator, v, degrees of freedom. The density function will give the height of the F distribution for a given value of F. 3. SAS (Statistical Analysis System) has functions to find an F value given the probability “p”, and numerator “ndf’ and denominator degrees of freedom “ddf’ and the noncentrality parameter “nc”and a function to find the probability of a certain F with numerator degrees of freedom, denominator degrees of freedom, and the noncentrality parameter. The commands are summarized below: SAS command to find F for a certain probability. F=FINV(p,ndf,ddf,nc); SAS command to find the probability of an F value. P=PROBF(F,ndf,ddf,nc); a. Write a program to compute the probability for any value of F. b. Write a program to compute the F for any p, ndf,ddf, and nc. c. What does the program below do? 210 is the SS, and 14.17 is the MS, for the Keppel one factor ANOVA example that we have used in class. data retpower; noncent=210/14.17; forit=finv(.95,2,12,0) ; power=1-probf (ferit,2,12,noncent) ; proc print; run; 
