Consider the experiment of picking one word at random from, Dissertation

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Consider the experiment of picking one word at random from

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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