Does Cross Validation Reduce Variance?

This significantly reduces bias as we are using most of the data for fitting, and also significantly reduces variance as most of the data is also being used in validation set.

How does cross-validation relate to variance?

The cross-validation estimator of, for example the prediction error, is defined as the average of the prediction errors obtained on each fold. Therefore, leave-one-out cross-validation has large variance in comparison to CV with smaller k.

What type of error does cross-validation reduce?

In the context of building a predictive model, I understand that cross validation (such as K-Fold) is a technique to find the optimal hyper-parameters in reducing bias and variance somewhat. Recently, I was told that cross validation also reduces type I and type II error.