Suppose Y is a continuous variable whose density gives the f

Suppose Y is a continuous variable whose density gives the following probabilities: Pr{ Y < -3 } = 0.05, Pr{ -3 < Y < -1 } = 0.15, Pr{ -1 < Y < 0 } = 0.3, Pr{ 0 < Y < 1 } = 0.3, Pr{ 1 < Y < 3 } = 0.15, Pr{ Y > 3 } = 0.05, Compute Pr{ Y > 0 }

Solution

Pr{ Y > 0 }=

Pr{ 0 < Y < 1 } + Pr{ 1 < Y < 3 } +, Pr{ Y > 3 }

= 0.3+0.15+0.05

= 0.50 (As these are mutually exclusive we can add them to get the required probability)