4. Suppose that the continuous random variables $(X, Y, Z)$ have a valid joint probability density function f(x, y, z) = Kxyz^2, 0 x, y 1, 0 z 3. Then, $E(Y) =$ (4) and E(Y|X = 1/2, Z = 1) = (5). Of course, you should find the value of $K$ first.

7. Let $X_1, \dots, X_n, X_{n+1}$ be a random sample from a normal population having an unknown mean $\mu$ and variance 1, and $\bar{X}_n$ be the average of the first $n$ variables. Then, the distribution of $X_{n+1} - \bar{X}_n$ is (8). If $\bar{X}_{200} = 5$, then the 95% confidence interval for $X_{201}$ is (9).

4. Suppose that the continuous random variables $(X, Y, Z)$ have a valid joint probability density function

$$f(x, y, z) = Kxyz^2, \quad 0 \le x, y \le 1, \quad 0 \le z \le 3.$$

Then, $E(Y) =$ (4) and $E(Y|X = \frac{1}{2}, Z = 1) =$ (5). Of course, you should find the value of $K$ first.

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相關試卷

4. Suppose that the continuous random variables $(X, Y, Z)$ have a valid joint probability density function $$f(x, y, z) = Kxyz^2, \quad 0 \le x, y \le 1, \quad 0 \le z \le 3.$$ Then, $E(Y) =$ (4) and $E(Y|X = \frac{1}{2}, Z = 1) =$ (5). Of course, you should find the value of $K$ first.

相關申論題

相關試卷

4. Suppose that the continuous random variables $(X, Y, Z)$ have a valid joint probability density function

$$f(x, y, z) = Kxyz^2, \quad 0 \le x, y \le 1, \quad 0 \le z \le 3.$$

Then, $E(Y) =$ (4) and $E(Y|X = \frac{1}{2}, Z = 1) =$ (5). Of course, you should find the value of $K$ first.