True mean of randomly-generated numbers?

I use GSL C++ library to generate random numbers now. The numbers obey a distribution, e.g. normal. So the expectation and std. deviation must be inputs, as well as the upper and lower bounds. It means if the generated number is not within the interval, then that number will be ignored.

The question is: someone said the input expectation and std. deviation are not true, because the pdf is truncated.

Are the inputs enough to represent the mean and std. deviation of random numbers? Is it a big difference between the inputs and true values? Is it anyway to analytically derive the true mean and std. deviation, with bounds?