Question: 1. Consider the random variable Y as defined above and a new random variable

Are the events Y = 1 and V = 1 independent?

2. Problem, and redo the problem using your new knowledge of independence and PIE.

Problem: In early December 2011, the Yarn Harlot felt "a mitten thing coming on" and, with eight colors of yarn-orange, red, yellow, lime green, forest green, robin's egg blue, indigo, and black-knitted a pile of mittens (true story). Suppose she knitted eight pairs of mittens, one left mitten and one right mitten of each base color, and placed them in the mitten box.

(a) Describe the state space of pulling a mitten from the box.

(b) What is P(left mitten)?

(c) What is P(cool color of mitten)? (Greens, blues, and purples are cool colors. Reds, oranges, and yellows are warm colors.)

(d) What is P((left mitten) or (cool color of mitten))?

(e) What is P((left mitten) and (cool color of mitten))?

(f) Design your own random variable R on this state space and compute E[R].