you received a large inheritance and would like to invest it by opening one or more restaurants. you have…

you received a large inheritance and would like to invest it by opening one or more restaurants. you have narrowed down your options to two, each of which have franchises that you could open in your location. we will call the options \restaurant x\ and \restaurant y\. suppose that x and y have the following properties: mean variance covariance e(x)=155 var(x)=18 cov(x,y)=8 e(y)=124 var(y)=20 a restaurant ? has higher expected revenue because ?. restaurant ? may see more varied revenue values because ?. as the revenue of restaurant x increases, the revenue of restaurant y is likely to ? because ?. b. find the correlation between x and y. (round your answer to 2 decimal places.) c. you decide you would like to invest in both restaurants. define a new variable z = x+y. calculate the expected value, variance, and standard deviation for the combined revenue of restaurants x and y. (round your answers to 2 decimal places.) mean variance standard deviation z = x+y e(z)= var(z)= a,=

you received a large inheritance and would like to invest it by opening one or more restaurants. you have narrowed down your options to two, each of which have franchises that you could open in your location. we will call the options \restaurant x\ and \restaurant y\. suppose that x and y have the following properties: mean variance covariance e(x)=155 var(x)=18 cov(x,y)=8 e(y)=124 var(y)=20 a restaurant ? has higher expected revenue because ?. restaurant ? may see more varied revenue values because ?. as the revenue of restaurant x increases, the revenue of restaurant y is likely to ? because ?. b. find the correlation between x and y. (round your answer to 2 decimal places.) c. you decide you would like to invest in both restaurants. define a new variable z = x+y. calculate the expected value, variance, and standard deviation for the combined revenue of restaurants x and y. (round your answers to 2 decimal places.) mean variance standard deviation z = x+y e(z)= var(z)= a,=

Answer

Explanation:

Step1: Calculate the expected value of (Z = X + Y)

The expected - value of a sum of two random variables is (E(Z)=E(X + Y)=E(X)+E(Y)). Given (E(X)=155) and (E(Y)=124), then (E(Z)=155 + 124=279).

Step2: Calculate the variance of (Z = X + Y)

The formula for the variance of the sum of two random variables is (Var(Z)=Var(X + Y)=Var(X)+Var(Y)+2Cov(X,Y)). Given (Var(X)=18), (Var(Y)=20), and (Cov(X,Y)=8), then (Var(Z)=18 + 20+2\times8=18 + 20 + 16=54).

Step3: Calculate the standard deviation of (Z)

The standard - deviation is the square - root of the variance. So (\sigma_Z=\sqrt{Var(Z)}=\sqrt{54}\approx7.35).

Step4: Calculate the correlation coefficient (\rho_{XY})

The formula for the correlation coefficient is (\rho_{XY}=\frac{Cov(X,Y)}{\sqrt{Var(X)Var(Y)}}). Substitute (Cov(X,Y) = 8), (Var(X)=18), and (Var(Y)=20) into the formula: (\rho_{XY}=\frac{8}{\sqrt{18\times20}}=\frac{8}{\sqrt{360}}\approx\frac{8}{18.97}\approx0.42).

Answer:

(E(Z)=279) (Var(Z)=54) (\sigma_Z\approx7.35) (\rho_{XY}\approx0.42)