Let f (x, y) 1/4 for 1 x 1 and 1 y

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Let f (x, y) Æ 1/4 for ¡1 · x · 1 and ¡1 · y · 1 (and zero elsewhere).

(a) Verify that f (x, y) is a valid density function.

(b) Find themarginal density of X.

(c) Find the conditional density of Y given X Æ x.

(d) Find E[Y j X Æ x].

(e) Determine P

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X2 ÅY 2 Ç 1

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(f ) Determine P[jX ÅY j Ç 2] .

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