3. Let X and Y be random variables with the following joint probability density function. f(X, Y) = e^-X, 0 < Y < X First derive E(Y | X), and then evaluate it at X = 2. What is the resulting expected value? (A) 1/2 (B) 1 (C) 2 (D) None of the above

2. Consider $yi = \beta0 + \beta1 Di + \beta2 xi + \beta3 (Di xi) + ui$, where $Di \in \{0, 1\}$ and $xi \in \mathbb{R}$, with $E(ui \mid Di, xi) = 0$. Define the conditional mean $\mu(D, x) = E(yi \mid Di = D, xi = x)$. Which statement is correct?(A) $ \beta_{1} = \mu (1,x) - \mu (0,x) $ for all $ x $(B) The marginal effect of $ x $ when $ D = 1 $ is $ \beta_{2} $(C) $ \beta{3} = \frac{\partial\mu(1,x)}{\partial x}\Big|{x = 0} - \frac{\partial\mu(0,x)}{\partial x}\Big|_{x = 0} $(D) $ \beta{2} + \beta{3} $ equals the intercept difference between $ D = 1 $ and $ D = 0 $

3. Let X and Y be random variables with the following joint probability density function. \( f(X, Y) = e^{-X} \), \( 0 < Y < X \) First derive \( E(Y | X) \), and then evaluate it at \( X = 2 \). What is the resulting expected value?
(A) \( \frac{1}{2} \)
(B) 1
(C) 2
(D) None of the above

相關試題

相關試卷

3. Let X and Y be random variables with the following joint probability density function. \( f(X, Y) = e^{-X} \), \( 0 < Y < X \) First derive \( E(Y | X) \), and then evaluate it at \( X = 2 \). What is the resulting expected value?(A) \( \frac{1}{2} \)(B) 1(C) 2(D) None of the above

相關試題

相關試卷

3. Let X and Y be random variables with the following joint probability density function. \( f(X, Y) = e^{-X} \), \( 0 < Y < X \) First derive \( E(Y | X) \), and then evaluate it at \( X = 2 \). What is the resulting expected value?
(A) \( \frac{1}{2} \)
(B) 1
(C) 2
(D) None of the above