Relationship between punctures and tube pressure What could be the relation between a bicycle's inner tube getting punctured and the pressure of the tube.  

Are they directly proportional? I.e, if the pressure of Bicycle tube is higher then it has higher chance of getting punctured.
It's not going to be directly proportional. Leaving aside the quality of the tyre and what it will be rated for, the shape of the graph is likely to be a U shape:


at the lower pressures the tube will be susceptible to puncture because it cannot repel sharps adequately, in addition really low pressures might let you trap the tube between the road and the rim.  
as the pressure increases, the tube and tyre will combine to actively repel sharps: the external object will need more and more pressure and exertion to break through, so becomes less and less likely to be able to do so 
at some point, though, the tube's pressure becomes so high, that the risk of a blowout increases: flaws in the tyre, the tube, especially around the valve, are more likely to be exploited, also that collisions e.g. with potholes, will be harder to accommodate. 


It's not going to be as simple as that, but might work as a general rule.