Example

Compute E( Y | X = 2) and var( Y | X = 2) for the data given in Example 4.

= 3f(Y = 3 | X = 2) + 6f(Y = 6 | X = 2) = 3(0.16/0.26) + 6(0.10/0.26) = 4.15

Note: f(Y = 3 |X = 2) = f(Y = 3, X = 2)/f(X = 2) = 0.16/0.26, and f(Y = 6 | X = 2) = f(Y = 6, X = 2)/f(X = 2) = 0.10/0.26, so var( Y | X = 2) = £[Y- E(Y | X = 2)]2 f(Y| X = 2)

= (3 - 4.15)2(0.16/0.26) + (6 - 4.15)2(0.10/0.26) = 2.13

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