Exercise 1:
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Write a function which takes a vector as an argument, checks that it is of type ‘numeric’ with values greater than or equal to 1 (if not, display an error message), and returns a data frame such that :
- the first column is this vector ;
- the second is the same vector in ascending order ;
- the third is the same vector in descending order ;
- the fourth is a vector of the same size containing the average (repeated);
- the fifth column contains a vector of letters such that, for each component x of the input vector, if the remainder of the Euclidean division of the integer part of x by 26 is k, then the corresponding value is the kth letter of the alphabet.

Test your function !

Exercise 2:
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1. a. Simulate a sample X of 100 independent random variables distributed according to a normal distribution in dimension 2 with expectation (0,0) and covariance matrix the identity matrix.
b. Do the same for Y but with expectation (3.3).
2. Plot these data on a graph.
3. Shuffle the Xs and Ys to form a new sample.
4. a. Calculate the pairwise Euclidean distance matrix of Z.
b. Run a clustering algorithm to see if the two sub-samples X and Y are found.

Exercise 3:
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Here's how high the tides will be in Bordeaux on Thursday 27 February (today!) :
Morning		0h	1h	2h	3h	4h	5h	6h	7h	8h	9h	10h	11h
Height (m)	1,31	0,82	0,47	1,13	2,71	3,88	4,87	5,36	4,76	3,71	2,85	2,16
Afternoon	12h	13h	14h	15h	16h	17h	18h	19h	20h	21h	22h	23h
Height (m)	1,54	0,97	0,48	0,14	1,99	3,25	4,38	5,15	4,96	3,95	3,02	2,33

1. Save this data to a file and import it into R.
2. Display the graph of heights as a function of time.
3. Run a regression (non-linear! cos... sin... ?) to find the parameters of a model you have defined.
4. Are the residuals normally distributed?