1. Take each problem in lect1 and write your own program to do it. You're welcome to look at my solution, but try to come up with at least one variant of what I did. 2. Find the median of a list of numbers on the command line. (The median is the middle number in the sorted order assuming there is an odd number in the list. If there is an even number in the list, then the median is the arithmetic mean of the two middle numbers.) Find the 95% confidence interval of the median using resampling/bootstrapping. q home1_2.q 29 87 47 29 13 3. Assume that the yield curve gives a different interest rate for different numbers of years out. For example, suppose that, for one year, the yield is 2% per annum; for two years, the yield is 2.1% per annum; then 2.4% per annum for three years. Now, write a program that takes a given set of payments over time followed by an underbar followed by a set of yield curve values of the same length. q home1_3.q 300 200 900 400 200 _ 2 2.1 2.4 2.5 2.6 4. Find the day of week of the first day of every month for a given year. q home1_4.q 2041 5. (Optional) Find the multiset intersection of a bunch of sets splits based on underbars. Multiset intersection keeps track of the counts. q home1_5.q foo bar foo foo _ zarf bar bar foo foo _ zarf bar bar bar foo foo bar foo foo bar