Question

Let $X_1, X_2, X_3$ be i.i.d. random variables from a continuous distribution having probability density function
$f(x) = \begin{cases} \frac{1}{2}x^{-3}, & \text{if } x > \frac{1}{2} \\\0, & \text{if } x \leq \frac{1}{2} \end{cases}.$
Let $X_{(1)} = \min\\{X_1, X_2, X_3\\}$. Then the value of $10E(X_{(1)})$ is equal to __________ (answer in integer).

Answer 1

The correct Answer is : 6 -6(Approx.)