A continuous random variableYhas cdf

F(y) =a+ay/ 2, − 2 <y< 0

1−be−cy3 ,y> 0

(a)Sketch the cdf whena= 1/2,b= 1/2 andc= 1.

Then deriveY'spdf generally, and sketch it whena= 1/2,b= 1/2 andc= 1.

Finally, write down the range of possible values fora,bandc.

(b)FindP(Y> −1|Y< 1) whena= 1/2,b= 1/2 andc= 1.