The random variable \(Y \sim U(0, X)\), where the marginal density of \(X\) isv
\( f_X(x) = \begin{cases} 2x & \text{for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases} \)
Then \(E(Y)\) is:
A random variable \(X\) has a cumulative distribution function \(F_X(x)\) given by
\( F_X(x) = \begin{cases} 0 & \text{if } x < 1 \\ \frac{x^{2} - 2x + 2}{2} & \text{if } 1 \le x < 2 \\ 1 & \text{if } x \ge 2 \end{cases} \)
Then \(E(X)\) is:
The area of bounded region R defined as \( R = \{(x,y): 0 < x < 2,\; 1 < y < 3,\; y > x \} \) is
Match List-I with List-II:
Match List-I with List-II. A data contains the following eight values:\[ 4,3,0,5,2,9,4,5 \]
Match List-I (Sample Statistics) with List-II (Population Parameters):