6. [16 points total] Suppose you have 26 cards labeled with the letters a through 2, shufed at random. You draw cards one at a time without replacement. (a) [3 points] Let T be the time at which the letter 1: appears.For example, if the cards drawn are c, 3,0, x,t, then T : 5. Calculate the distribution of T. (b) [7 points] Let X be the number of vowels (the letters a, e, i, o, u) that appear before the letter t. For example, if the cards drawn are c,a,o,x,t,... then X : 2. Calculate E[X]. (c) [6 points] Let C be the time at which the letter c appears, and T is still dened as before. For example, if the cards drawn are c, 3,0, x,t, then C : 1 and T : 5. Is the correlation Corr(C, T) positive, negative, or zero? You do not need to calculate it numerically, but you should justify your