Homework Problem Set 1, Due Friday September 4, 2016.
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Homework Problem 1, STAT 705, Fall 2015.

Assigned 8/29/2016,  Due 9/4/2016

[But since the due-date was ambiguous in the original assignment,
homeworks received by 9/7/2016 will also be accepted as on-time.]

For each of the following problem parts, your submitted HW solution 
should contain (a few) R code lines, together with at least one 
more code line showing IN BRIEF that your code works as desired. 
LENGTHY OUTPUTS ARE DISCOURAGED -- YOU MAY OF COURSE GENERATE THEM 
FOR YOUR OWN CHECKING, BUT I AM LOOKING FOR BRIEF WAYS TO VERIFY 
SOME NON-OBVIOUS ASPECT (your choice) OF THE R OBJECTS YOU GENERATE.

(a) Give the R code lines to create a single long integer vector 
named LongI in your workspace, consisting of:

   the 4-tuple (3,7,6,9) appearing 25 times followed by the arithmetic 
   progression from 273 down to 0 (inclusive) by 3's, with this whole 
   sequence repeated 10 times alternately in forward and reverse order.

Relevant R commands: "rep", "rev"


(b) In the vector you generate in (a), give the 777'th and 1000'th 
elements.


(c) Give a table of the frequencies of occurrence of all of the 
decimal digits 0,...,9 in all components of your vector in (a).

HINT: make a long character string out of your concatenated integer
vector, and then split it into individual characters and change 
those back to numbers.

Relevant R commands: "table", "paste", "strsplit", "unlist"


(d) Create a data-frame "Dfr" consisting of the following 3 columns:

column 1, named "TorF": a logical vector of length 120 consisting 
    of TRUE/FALSE values corresponding to the condition  
    sin(3*k^2 - 7) > 0 for k=1,..,120

column 2, named "Sums": a numeric vector giving the partial sums 
    for j=1 up to k of sin(3*j^2 - 7) ,  as k ranges from 1 to 120

column 3, named "Grades": a character vector containing respectively 
    "A","B","C","D","F" in every position k where the column 2 value 
    falls in the ranges (-1,Inf), (-3,-1], (-5,-3], (-7,-5], (-Inf,-7]

PRINT ONLY A FEW LINES OF YOUR DATA-FRAME, and verify that the columns 
have the desired variable types.

Relevant R commands:  "cumsum", "class"