Respuesta :
Answer:
(a) The expected cash flow from Palmer Heights is $30,000 and from Crenshaw Village is $25,000.
(b) The coefficient of variation for Palmer Heights is 43.47% and for Crenshaw Village is 31%.
Step-by-step explanation:
The formula to compute the expected value of a discrete probability distribution is:
[tex]E(X)=\sum x.P(X=x)[/tex]
The formula to compute the variance of a discrete probability distribution is:
[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}[/tex]
The formula to compute the coefficient of variation is:
[tex]CV=\frac{SD(X)}{E(X)}\times 100[/tex]
Denote:
X = Palmer Heights
Y = Crenshaw Village
(a)
Compute the expected cash flow from Palmer Heights as follows:
[tex]E(X)=\sum x.P(X=x)\\=[(10\times0.1)+(15\times0.2)+(30\times0.4)+(45\times0.2)+(50\times0.1)]\\=30[/tex]
Compute the expected cash flow from Crenshaw Village as follows:
[tex]E(Y)=\sum y.P(Y=y)\\=[(15\times0.2)+(20\times0.3)+(30\times0.4)+(40\times0.1)]\\=25[/tex]
Thus, the expected cash flow from Palmer Heights is $30,000 and from Crenshaw Village is $25,000.
(b)
Compute the standard deviation of cash flow from each apartment as follows:
[tex]SD(X)=\sqrt{E(X^{2})-(E(X))^{2}} \\=\sqrt{\sum x^{2}P(X=x)-(30)^{2}}\\=\sqrt{1070-900}\\=\sqrt{170}\\=13.04[/tex]
[tex]SD(Y)=\sqrt{E(Y^{2})-(E(Y))^{2}} \\=\sqrt{\sum y^{2}P(Y=y)-(25)^{2}}\\=\sqrt{685-625}\\=\sqrt{60}\\=7.75[/tex]
Compute the coefficient of variation for Palmer Heights as follows:
[tex]CV=\frac{SD(X)}{E(X)}\times 100=\frac{13.04}{30}\times100=43.46667\approx43.47\%[/tex]
Compute the coefficient of variation for Crenshaw Village as follows:
[tex]CV=\frac{SD(Y)}{E(Y)}\times 100=\frac{7.75}{25}\times100=31\%[/tex]
Thus, the coefficient of variation for Palmer Heights is 43.47% and for Crenshaw Village is 31%.
