The discussion centers on calculating the probability P[X ≥ 1/2 | θ > 1] for a random variable X defined by the density function f(x; θ) = θ x^(θ - 1) I(0,1)(x), where θ > 0. Participants seek clarification on how to structure the solution to this probability problem, specifically under the condition that θ is greater than 1. The key takeaway is that understanding the implications of the density function and the condition on θ is crucial for solving the probability query.
PREREQUISITESStatisticians, data scientists, and students in probability theory who are looking to deepen their understanding of conditional probabilities and density functions.
safina said: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