1. The random variable X has distribution function Check whether there is a subinterval of on which [0,∞) F(x) is DFR. 2. Consider lifetimes X and Y with the respective probability densities With the...

1. The random variable X has distribution function

Check whether there is a subinterval of on which [0,∞) F(x) is DFR.

2. Consider lifetimes X and Y with the respective probability densities

With the notation introduced in section 1.4, let X2 and be the corresponding resi- Y₂
dual lifetimes given that and respectively.