"Convergence in probability" is a technical term in relation to a series of random variables. Not clear whether this was your question though, I suggest providing more context.

It might help if you specified why WHAT was important in random variables.

Michael O'Flynn has written:

'Probabilities, random variables, and random processes' -- subject(s): Probabilities, Random variables, Signal processing, Stochastic processes

the statistically independent random variables are uncorrelated but the converse is not true ,i want a counter example,

A random process is a sequence of random variables defined over a period of time.