6. The continuous random variable \(Y\) has a uniform distribution on [ 0,2 ].
- It is given that \(\mathrm { E } [ a \cos ( a Y ) ] = 0.3\), where \(a\) is a constant between 0 and 1 , and \(a Y\) is measured in radians.
Determine the value of the constant \(a\).
- Determine the \(60 ^ { \text {th } }\) percentile of \(Y ^ { 2 }\).
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