4. Show that if a nite list consists only 0's and 1's then the variance of the list must be the product of the proportions of the 0's and the 1's in the list. You may denote the proportion of 1's as p. (3 points) 5. Now consider a new list obtained by transforming the list in the previous problem. The new list is created bydoubling each element of the old list and then adding 1. That is, if 3,- represents the old list and y; the new one, yi = 2.1.} + 1. \"That is the varianoe of the new list in terms of the proportions of the 0's and 1's of the original list? (3 points) 6. Soccer players are among the highest paid athletes in the world, if you oount endorsements. Cristiano Ronaldo of Real Madrid, earned the highest salary at $17 million in 2012, but let's look at Major League Soccer salaries. The average MLS salary in 2012 was about $179,200, and the SD was about $455,409. The fraction of the salaries in the original list that are greater than $1,000,000 cannot be greater than . (3 points)