1. Consider the following sample information for variable \(\mathrm{X}\), where \(\text{A}\) = Asians, \(\mathrm{E}=\) Europeans, \(\mathrm{t}=\mathrm{time}\) :

1. Derive and draw X's probability distribution.
2. Compute X's mean, variance, standard deviation, median and mode.
3. Draw X's Box-and-Whiskers Plot.
4. Group X into 4 intervals and derive and draw the histogram.
5. Draw X's time graph.
6. For X, compute the grouped mean, grouped variance and grouped standard deviation.
7. Derive and draw A's and B's probability distributions in terms of X.
8. Using the corresponding values for X, compute A's and B's means, variances, standard deviations, medians and modes.
9. Using the corresponding values for X, draw A's and B's Box-and-Whiskers Plots in the same diagram.

(2) Let \(\mathrm{Y}=2+5 \mathrm{X}^{2}, \mathrm{~W}=3+6 \mathrm{Z}^{2}\) (where \(\mathrm{Y}, \mathrm{X}, \mathrm{W}\) and \(\mathrm{Z}\) are all random variables) and data for \(\mathrm{X}\) and \(\mathrm{Z}\) be as follows: \([\mathrm{X}: 4,5,7,1]\) and \([\mathrm{Z}: 8,3,6,9]\)

Compute the following: \(E(Y), E(W), \operatorname{COV}(Y W), \operatorname{CORR}(\mathrm{YW}), \operatorname{VAR}(2 \mathrm{Y}+0.5 \mathrm{~W})\).

(3) A portfolio of risky investments consists of stocks \(\mathrm{Y}\) and \(\mathrm{X}\) with the following sample holding period returns (where t=time):

1. Draw a time diagram displaying \(\mathrm{Y}\) and \(\mathrm{X}\) in the same graph.
2. Compute the correlation coefficient between \(\mathrm{Y}\) and \(\mathrm{X}\) and draw the scatter plot with a representative line through it.
3. Draw the Efficient Frontier of the portfolio and identify the spending percentages that minimize risk.

Price: $21.04

Solution: The downloadable solution consists of 16 pages, 504 words and 18 charts.
Deliverable: Word Document