Calculating Probability for X from f(x;θ) with θ > 0

[safina]

Let X be a single observation from the density f\left(x;\theta\right) = \theta x^{\theta -1}I_{(0,1)} (x), where \theta > 0. What is the P\left[X \geq \frac{1}{2} |\theta > 1|\right]?

Please help me structure the solution of this problem

 

[statdad]

Let X be a single observation from the density f\left(x;\theta\right) = \theta x^{\theta -1}I_{(0,1)} (x), where \theta > 0. What is the P\left[X \geq \frac{1}{2} |\theta > 1|\right]?

Please help me structure the solution of this problem

What do you mean by

<br /> P\Big(X \ge \frac 1 2 |\theta &gt; 1 |\Big)<br />