please answer the question quickly

QUESTION 4 (a) A pension fund must pay $1,000 at the end of each of the next five years. Find the Present Value and Duration for this set of payments when the interest rate used to find the discounted value is 0.05 or 5 %. (b) Suppose the pension fund invests in a portfolio of two- and five-year zero-coupon bonds and needs to satisfy the conditions to immunize its bond portfolio. It uses this portfolio to make these five payments of $1,000. Find the proportion of the fund allocated to two-year bonds. (2 + 2 = 4 marks) QUESTION 5 (a) If you roll a dice five times what is the probability that you will roll more than one 6? (b) If you roll a dice five times what is the mean and the variance of the number of 6s you will throw? Please use the Binomial formulas (Mean = n.p, Variance = n.p.(1 - p)) to work these out and then check using the general formulas for the mean and variance of any probability distribution: H= EXP(X;) and 1=1 52 = [(Xi - H ) 2 P ( Xi ) (c) If you roll a dice five times what is the skewness and the kurtosis of the number of 6s you will throw. (d) If you roll a 50-sided dice 20 times what is the mean and the variance of the number of 6s you will throw? (e) Again, rolling your 50-sided dice 20 times, what is the probability of getting three 6s