Consider random variable X = {0,1} with Pr(X) = 0, Pr( X = 1) both are strictly positive. In this case we say X is a nondegenerate binary random variable. Consider the linear regression model Y = Bo + B1X +U You may assume all moments are well-defined. There is a markdown cell right below each prompt. Type your solutions in the markdown cells. (a) Show that E[Y|X] = a +bX Find expressions for a and b. (b) Suppose E[XU] = E[U] = 0 Show that E[U|X] = 0, and E* [Y|X] = E[Y|X] (c) Consider a random variable X = {1,2,3,4}, such that X = 1 if female, finished college 2 if female, did not finish college 3 if male, finished college 4 if male, did not finished college Construct linear regression model Y = D"B1 + U such that D= D D D3 where D, D2, D3 are binary random variables. where D1, D2, D3 are binary random variables. (d) Continuing from (c), show that E[Y|D] = a + b Di + cD2 + dD3. Assuming E[DU] = 03 , show that E[U|D] = 0, and E* [Y|D] = E[Y|D). (e) Suppose E[Y|X] = XTB. Show that E* [Y|X] = E[Y|X]. Consider random variable X = {0,1} with Pr(X) = 0, Pr( X = 1) both are strictly positive. In this case we say X is a nondegenerate binary random variable. Consider the linear regression model Y = Bo + B1X +U You may assume all moments are well-defined. There is a markdown cell right below each prompt. Type your solutions in the markdown cells. (a) Show that E[Y|X] = a +bX Find expressions for a and b. (b) Suppose E[XU] = E[U] = 0 Show that E[U|X] = 0, and E* [Y|X] = E[Y|X] (c) Consider a random variable X = {1,2,3,4}, such that X = 1 if female, finished college 2 if female, did not finish college 3 if male, finished college 4 if male, did not finished college Construct linear regression model Y = D"B1 + U such that D= D D D3 where D, D2, D3 are binary random variables. Consider random variable X = {0,1} with Pr(X) = 0, Pr( X = 1) both are strictly positive. In this case we say X is a nondegenerate binary random variable. Consider the linear regression model Y = Bo + B1X +U You may assume all moments are well-defined. There is a markdown cell right below each prompt. Type your solutions in the markdown cells. (a) Show that E[Y|X] = a +bX Find expressions for a and b. (b) Suppose E[XU] = E[U] = 0 Show that E[U|X] = 0, and E* [Y|X] = E[Y|X] (c) Consider a random variable X = {1,2,3,4}, such that X = 1 if female, finished college 2 if female, did not finish college 3 if male, finished college 4 if male, did not finished college Construct linear regression model Y = D"B1 + U such that D= D D D3 where D, D2, D3 are binary random variables. where D1, D2, D3 are binary random variables. (d) Continuing from (c), show that E[Y|D] = a + b Di + cD2 + dD3. Assuming E[DU] = 03 , show that E[U|D] = 0, and E* [Y|D] = E[Y|D). (e) Suppose E[Y|X] = XTB. Show that E* [Y|X] = E[Y|X]. Consider random variable X = {0,1} with Pr(X) = 0, Pr( X = 1) both are strictly positive. In this case we say X is a nondegenerate binary random variable. Consider the linear regression model Y = Bo + B1X +U You may assume all moments are well-defined. There is a markdown cell right below each prompt. Type your solutions in the markdown cells. (a) Show that E[Y|X] = a +bX Find expressions for a and b. (b) Suppose E[XU] = E[U] = 0 Show that E[U|X] = 0, and E* [Y|X] = E[Y|X] (c) Consider a random variable X = {1,2,3,4}, such that X = 1 if female, finished college 2 if female, did not finish college 3 if male, finished college 4 if male, did not finished college Construct linear regression model Y = D"B1 + U such that D= D D D3 where D, D2, D3 are binary random variables