Finding the fraction of sample value Y that lie in the interval (0.9,1.9]
I am having trouble finding the sample value of Y that lie in the interval (0.9,1.9]. I have been able to determine the sample average and the sample variance; however, the last portion is evading me at the moment.
Here are the instruction I received. In case 3, assume that X1 has the same uniform distribution as in case 1, and that X2 is described by the density function specified (and X1 and X2 are independent). Calculate the sample average, sample variance, and the fraction of sample values Y that lie in the interval (0.9,1.9].
case 1) X~U(0,1) E(Y) = 1 V(Y) = 1/6 P(0.9<Y<=1.9) = 0.59
case 3) 0 (t<0)
f(t) = 3t^2 (0<=t<=1) E(Y) = 1.25 V(Y)= 0.12083 P(0.9<=Y<=1.9) = ?
Any Help would be greatly appreciated