Discuss the below:
Q: a) Compute Ex, Ex^2, Ey, Ey^2
Ex=103
Ex^2=3241(11)^2+(36)^2.....)
Ey=90
Ey^2=2024
x: 11 0 36 21 31 23 24 -11 -11 -21
y: 10 -2 29 14 22 18 14 -2 -3 -10
b) Find mean, variance, standard deviation.
For x: (mean) I add all numbers and divide by 10
So x= Ex/10=10.03
So y=Ey/10=9
For the sample variance For standard deviation
The denominator is n-1=9 s^2 = { Ex^2 - [(Ex)^2 / n] } / n-1 s^2 = { Ex^2 - [(Ex)^2 / n] } / n-1
s^2 = { 3241 - [(103)^2 / 10] } / 10-1 s^2 = { 2024 - [(90)^2 / 10] } / 10-1
s^2 = { 3241 - [10609/ 10] } / 9 s^2 = { 2024 - [8100/ 10] } / 9
s^2 = { 3241 - [1060.9] } / 9 s^2 = { 2024 - 810] } / 9
s^2 = { 2180.1 } / 9=242.2333 which=15.56 s^2 = 1214 / 9=134.88=11.61
c) compute 75% chebyshev interval around the mean of x and y values. Use the intervals to compare two funds.
d) Compute the coefficient of variation of each fund. If s represents risks and the x(mean) represents expected return, then s√x can be the measure of risk per unit of expected return. Why is the smaller cv better?