Question

(b) The Art department decided to order some painting sets. Each set contains one packet of paper and 3 coloring ink pens. Packets of paper normally have 20 sheets each, but 5% of packets are overfull and have more than 20 sheets of paper. In addition, each ink pen has a 2% chance of leaking during shipping Assume that the painting sets are packed one at a time into a shipping box, up to and including the first set with an overfull packet of paper. Let X be the number of painting sets packed into the box that are not overfull. In addition, let Y be the total number of pens in the box that leak during shipping. Note that Y includes leaky pens from the last gift box (if any), whereas X does not include the last gift set. You should assume in this question that whether or not each packet of paper is overfull, and whether or not each pen leaks, are all independent. i. Write down the conditional distribution of Y given {X-r), including parameter(s) (2 marks each) ii. Find E(Y|X) 1 mark each ii. Find E(Y) (1 mark each) iv. Find Cov(X, Y) 2 marks each

Answer 1

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