ST790R -- Fall 2009

  Homework #4 -- due Tuesday, 13 October 2009
   
  Exercises in Textbook: (*just turn in these)
   6.25*(modified) Compute the SVD of X and X+E for 3 different sizes
    of 'small' and see if change in singular values matches the results
    of (6.7.4).  Use the cork data again for X, but add as the fifth
    (or zero-th) column a column of ones for the intercept.
   7.24* (write code in R using multiplications -- compare to
    formula with gamma functions)

  R Exercises:

  *1) Compute the following probabilities or related functions
     at these six x values  +/-3, +/-6, +/-12
    a) Pr(X < x) where X is Normal(0,1)
    b) log of the probabilities in (a)
    c) log(1 + exp(x))
    d) Pr(X < x ) where X is Student's t with 7 df
    e) Pr(X < x ) where X is Gamma(shape=5, scale=1) (just positive x)
    f) Pr(X < x ) where X is F with 3 and 5 df (just positive x)
    g) mark those whose value is suspect (not very accurate) or
        useless (e.g. zero when a good value can be found)
   R gives several probability functions: pnorm, etc., pt, pgamma, pbeta.