P0077_Soln - P0077_Soln.doc If two random variables are...

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Unformatted text preview: P0077_Soln.doc If two random variables are independent, then pXY ( x, y ) = pX ( x ) pY ( y ) Compute the marginals for these data as in P0079 and P0080 and can see that this relationship does not hold. The RVs are dependent. N prob 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0.0 4 6 0 11 0.0 6 7 0 12 0.1 2 13 0.1 6 14 0.2 0 15 0.1 8 16 0.1 4 17 0.0 8 18 0.0 2 1 9 0 20 0 Days prob 0 0.0 8 1 0.2 6 2 0.3 2 3 0.2 2 4 0.1 0 5 0.0 2 Number of Days with Headache Number of Niripsa Tablets 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 For example, 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 2 5 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3 2 6 5 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 4 2 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 P0077_Soln.doc pXY ( x, y ) ¹ pX ( x ) pY ( y ) 0.06 ¹ (0.12)(0.32) 0.06 ¹ 0.0384 ...
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