true/ false for these parts of a question with explanation

Under the assumption that sampled monthly returns of an asset follow a normal distribution, the estimates of the variance of monthly returns also follow a normal distribution The beta of a portfolio is a weighted average (with weights being the asset weights) of the betas of the assets in the portfolio. Suppose that all idiosyncratic errors are correlated with correlation coefficient p=1 in APT. In this case, we could not say that idiosyncratic risk can be diversified away by investing in a well-diversified portfolio