problem_set2 - EE 511 Problem Set 2 Due on 3 Sep 2007 1 A...

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EE 511 Problem Set 2 Due on 3 Sep 2007 1. A and B are two events. Which is larger, P [ AB | A ] or P [ AB | ( A + B )]? 2. Events A and B are mutually exclusive. Can they be independent? 3. Consider a random variable X with the property that a X ( s ) b for all s belonging to the sample space S . Which statement(s) is(are) true? (a) F X ( x ) = 0 for x < a , (b) F X ( x ) = 0 for x > b , (c) F X ( x ) = 1 for x > a , and (d) F X ( x ) = 1 for x > b . 4. Consider a random variable X with pdf f X ( x ) given by f X ( x ) = c (1 - x 2 ) - 1 x 1 0 else (i) Find c such that f X ( x ) is a valid pdf, and (ii) calculate P [ X > 0], P [ X < 1 / 2] and P [ | X | > 0 . 75]. 5. Which of the following functions can be the probability density function of a random variable? (i) f ( x ) = x for - 1 x 1 and f ( x ) = 0 otherwise, (ii) f ( x ) =
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