Please explain answers- using for test review!!

Let X be a dummy variable equal to one if the student is an international student and zero otherwise, and Y is a dummy variable equal to one if the student majored in economics and zero otherwise, with the following joint pdf: PX,Y(x,y)=5xy+1, where Y={1,0} and X={1,0} : a. [5 points] Derive the covariance between X and Y. Derive the variance of X. (write the formula and then find the covariance - NOT ENOUGH TO JUST WRITE THE FINAL VALUES) b. [5 points] Derive the conditional expectation function (CEF): E[YX] (again write the formula first NOT ENOUGH TO JUST WRITE THE FINAL VALUES) c. [15 points] The linear regression model is defined as =Var(X)Cov(X,Y) and =E[Y]E[X]. What is the population linear regression model in this example? (write the formula and then derive the values) BONUS QUESTION - [5 points] Compare E[YX=1] with the value you would get for +X, where X=1. What if X=0 ? Are the values the same? Can you explain your result in line with what we learned in class? Let X be a dummy variable equal to one if the student is an international student and zero otherwise, and Y is a dummy variable equal to one if the student majored in economics and zero otherwise, with the following joint pdf: PX,Y(x,y)=5xy+1, where Y={1,0} and X={1,0} : a. [5 points] Derive the covariance between X and Y. Derive the variance of X. (write the formula and then find the covariance - NOT ENOUGH TO JUST WRITE THE FINAL VALUES) b. [5 points] Derive the conditional expectation function (CEF): E[YX] (again write the formula first NOT ENOUGH TO JUST WRITE THE FINAL VALUES) c. [15 points] The linear regression model is defined as =Var(X)Cov(X,Y) and =E[Y]E[X]. What is the population linear regression model in this example? (write the formula and then derive the values) BONUS QUESTION - [5 points] Compare E[YX=1] with the value you would get for +X, where X=1. What if X=0 ? Are the values the same? Can you explain your result in line with what we learned in class? Let X be a dummy variable equal to one if the student is an international student and zero otherwise, and Y is a dummy variable equal to one if the student majored in economics and zero otherwise, with the following joint pdf: PX,Y(x,y)=5xy+1, where Y={1,0} and X={1,0} : a. [5 points] Derive the covariance between X and Y. Derive the variance of X. (write the formula and then find the covariance - NOT ENOUGH TO JUST WRITE THE FINAL VALUES) b. [5 points] Derive the conditional expectation function (CEF): E[YX] (again write the formula first NOT ENOUGH TO JUST WRITE THE FINAL VALUES) c. [15 points] The linear regression model is defined as =Var(X)Cov(X,Y) and =E[Y]E[X]. What is the population linear regression model in this example? (write the formula and then derive the values) BONUS QUESTION - [5 points] Compare E[YX=1] with the value you would get for +X, where X=1. What if X=0 ? Are the values the same? Can you explain your result in line with what we learned in class? Let X be a dummy variable equal to one if the student is an international student and zero otherwise, and Y is a dummy variable equal to one if the student majored in economics and zero otherwise, with the following joint pdf: PX,Y(x,y)=5xy+1, where Y={1,0} and X={1,0} : a. [5 points] Derive the covariance between X and Y. Derive the variance of X. (write the formula and then find the covariance - NOT ENOUGH TO JUST WRITE THE FINAL VALUES) b. [5 points] Derive the conditional expectation function (CEF): E[YX] (again write the formula first NOT ENOUGH TO JUST WRITE THE FINAL VALUES) c. [15 points] The linear regression model is defined as =Var(X)Cov(X,Y) and =E[Y]E[X]. What is the population linear regression model in this example? (write the formula and then derive the values) BONUS QUESTION - [5 points] Compare E[YX=1] with the value you would get for +X, where X=1. What if X=0 ? Are the values the same? Can you explain your result in line with what we learned in class