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Unformatted text preview: (b) If selected ball is red ﬁnd the probability that it was selected from the yellow box. (c) If selected ball is blue ﬁnd the probability that it was selected from the white box. 4. Let f ( x,y ) = ce-x 2 + y 2-2 x-7 y 2 ,-∞ ≤ x,y ≤ ∞ , be the joint pdf of random variables X and Y . (a) Determine the value of the constant c . (b) Are X and Y independent random variables? Explain. (c) Compute E ( Y 2 + X 2 Y ). 5. Let X be exponentially distributed random variable with parameter λ . Clearly, f ( x ) = λe-λx ,x ≥ 0. Further, let Y be uniform random variable deﬁned on the interval [ a,b ], i.e., p ( y ) = ( 1 b-a a ≤ y ≤ b otherwise . Let Z be the standard normal random variable with pdf f ( z ) = 1 √ 2 π e-z 2 2 ,-∞ ≤ z ≤ ∞ . Assuming that X , Y , and Z are independent ﬁnd E ((2 XZ-4 Y-1 ) 2 + XY + Z 2 √ Y ). 1...
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This note was uploaded on 05/06/2011 for the course IE 336 taught by Professor Bruce,s during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08