Solution to HW set 7.
======================

(a) 
> cathed = read.table(file="cathed.txt")   
                  ## after editing in word-processed file
  names(cathed) = c("Town","Style","Height","Length")
        ### 25 x 4: first col is factor of town names
  cathed2 = cathed[order(cathed$Length),]
> plot(cathed2[,4], cathed2[,3], type="n", xlab="Length (feet)",
    ylab="Height (feet)", main=
    "English Cathedral Heights vs Lengths, by Style")
  points(cathed2[cathed2[,2]==0,4],cathed2[cathed2[,2]==0,3], pch=5, type="b")
  points(cathed2[cathed2[,2]==1,4],cathed2[cathed2[,2]==1,3], pch=18, type="b")
  legend(locator(), legend=c("Romanesque","Gothic"),
       pch=c(5,18), lty=c(3,1))


(b) 
> xtmp = rgamma(1600, shape=3.5)
  round(quantile(xtmp, probs=c(.9,.99,.996, .999)),2)  90%   99% 99.6% 99.9%
 6.22  9.69 10.83 11.56
#### choose max = 12, only one obs is larger: replace it my 12
  hist(pmin(xtmp,12), breaks=seq(0,12,by=12/40), prob=T, xlim=c(0,12), 
      xlab="Gamma Variates", ylab="Scaled relative frequency",
      main=paste("Scaled Histogram of Gamma Variates","\n",
              "with overlaid Gamma(3.5,1) density"))
  curve(dgamma(x,3.5), add=T, lty=3)