In beta distribution, for alpha=4, beta=3 & X=0.5 we get value 1.875 But probability should be less than one l. Can anybody explain this?
The value of the pdf is 1.875, but as that isn't a probability, it can be greater than 1. A probability is an integral of the pdf between an upper and lower bound. There's nothing particularly special about the Beta distribution here. For example, consider the uniform distribution over the range [0,0.1]. Here, the pdf is f(x) = 10 for 0<x<0.1.