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1. Consider the experiment of picking one word at random from the sentence

ALL IS WELL IN THE NEWELL FAMILY

Let X be the length of the word selected and Y the number of L's in it. Find in tabular form the joint pmf of Xand Y , their marginal pmfs, means, and variances, and the correlation between X and Y .

2. A fair coin is tossed four times. Let X be the number of heads, Z the number of tails, and Y D jX - Zj. Find the joint pmf of .X; Y /, and E.Y /.

3. Consider the joint pmf p.x; y/ D cxy;1 :S x :S 3; 1 :S y :S 3.

(a) Find the normalizing constant c.

(b) Are X and Y independent? Prove your claim.

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