Please answer the following question!

6. (10 pts each) Indicate whether the following statements are true or false [circle one]. Use 1 or 2 sentences to discuss whyr it is so. (a) From the ARCH model in (I), let's now assume 1} = 016;, e; N iid t(5) where H5) indicates the t-distribution with the degrees of freedom 5. This ARCH model with the t- distributed hmm'ation, we can generate the asymmetric responses of :1": to the positive and negative shocks of 8:, so is more popular than the model in [1) in practice. True False Why? (b) The single index model in ('2) has been extended to include a few more factors recently. These additional factors in the multi-factor models are designed to capture the idiosyncratic risks from Ea, while the market-wide risk is still soler captured by RM; True False Why? (c) Assume X ~ Bernoulli (1/2), and Y ~ PHI/2,1) hence EOE] = E(Y) = 1/2.For any given random variable Z that is statistically indendent of X and Y, E [Z (X Y)] 99 U because X 96 Y. True False Why