[See Solution] A density function sometimes used by engineers to model lengths of life of electronic components is the Rayleigh density, given by f(y)=


Question: A density function sometimes used by engineers to model lengths of life of electronic components is the Rayleigh density, given by

\[f(y)= \begin{cases}\left(\frac{2 y}{\theta}\right) e^{-y^{2} / \theta}, & y>0 \\ 0, & \text { elsewhere }\end{cases}\]
  1. If \(Y\) has the Rayleigh density, find the probability density function for \(U=Y^{2}\).
  2. Use the result of part (a) to find \(E(Y)\) and \(V(Y)\).

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