TWO

(1) Using excel, generate 1000 values in a column, using the formula

=-10 *LN (RAND ())

(a)Compute descriptive statistics about the data in that column include the minimum value, the maximum value, the mean, themedian and the standard deviation.

(b)Tabulate the values into 10 BINS, each of width equal to 5, the first BIN beginning at 0, and the eleventh BIN for overflow (if any)

(c)Does the histogram resemble anydistribution with which you are familiar? If so what is the name?

(2) Use excel to devise a monte Carloexperiment to estimate the value of ,as in the equation for the area, HINT: consider a quarter of a circle with unit radius inside a unit square. Throw a random dart onto the unit square.

(3) Using excel generate 12 columns, eachwith 250 values using the formula =RAND ().In cell M1, place the formula

=SUM (A1:L1)-6 and copy it to the 249 cells below M1 in Colum

M.

(a)Compute the descriptive statistics about data in column M,

Including minimum value, maximumvalue, mean, median and

Standard deviation.

(b)Tabulate the values with 9 BINS, thefirst bin will include all

Values less than or equal to -3.5; the next 6 BINS are of

Width one; the last BIN will include all values greater than

3.5.

(c)Does the histogram resemble any distribution with which

You are familiar? If so what is the name?

TOTAL: [20MKS]