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The median of the distribution of a continuous random
Chapter 4, Problem 42E(choose chapter or problem)
The median of the distribution of a continuous random variable Y is the value \(\phi_{.5}\) such that \(P\left(Y \leq \phi_{.5}\right)=0.5\). What is the median of the uniform distribution on the interval \(\left(\theta_{1}, \theta_{2}\right)\)?
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QUESTION:
The median of the distribution of a continuous random variable Y is the value \(\phi_{.5}\) such that \(P\left(Y \leq \phi_{.5}\right)=0.5\). What is the median of the uniform distribution on the interval \(\left(\theta_{1}, \theta_{2}\right)\)?
ANSWER:Step 1 of 2
It is given that Y is a continuous random variable and the median of distribution of Y is \(phi_{0.5}\).
Also it is given that \(\mathrm{P}\left(\mathrm{Y} \leq \phi_{0.5}\right)=0.5\)
Using this we need to find the median of the Uniform distribution on the interval \(\left(\theta_{1}, \theta_{2}\right)\).
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