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ID: 18399

Nhận biết (M1)
Assume two people are waiting in the same line for a bank teller. Let $\displaystyle X_1$ be the time at which person 1 completes his business and let $\displaystyle X_2$ be the time at which person 2 completes his business. Since person 1 is in front of person 2, he will be finished first and certainly $\displaystyle X_1 < X_2$ . The joint density for $\displaystyle (X_1, X_2)$ is
$\displaystyle f_{X_1,X_2}(x_1, x_2) = \begin{cases} 9e^{-3x_2}, & 0 < x_1 < x_2, \\ 0, & \text{otherwise.} \end{cases}$
(a) Find the margine density function $\displaystyle f_{X_1}(x_1)$ for $\displaystyle X_1$ .
(b) Find $\displaystyle E(X_2|X_1 = x_1)$ .

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