- The continuous random variable \(X\) is uniformly distributed over the interval \([ a , b ]\) where \(0 < a < b\)
Given that \(\mathrm { P } ( X < b - 2 a ) = \frac { 1 } { 3 }\)
- show that \(\mathrm { E } ( X ) = \frac { 5 a } { 2 }\)
- find \(\mathrm { P } ( X > b - 4 a )\)
The continuous random variable \(Y\) is uniformly distributed over the interval [3, c] where \(c > 3\)
Given that \(\operatorname { Var } ( Y ) = 3 c - 9\), find
- the value of \(c\)
- \(\mathrm { P } ( 2 Y - 7 < 20 - Y )\)
- \(\mathrm { E } \left( Y ^ { 2 } \right)\)