HW04_2011 - for & < x <...

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PROF. HONG FALL 2011 ECONOMICS 6190 PROBLEM SET # 4 1. Let f ( x ) = c x for x = 1 ; 2 ; ::: and c c so that f ( x ) is a valid PMF? If yes, give the value of c: Otherwise, explain why not. 2. Suppose a discrete random variable X has the CDF F ( x ) = 8 > > > > > > < > > > > > > : 0 ; x < 1 ; 0 : 4 ; 1 x < 3 ; 0 : 6 ; 3 x < 5 ; 0 : 8 ; 5 x < 7 ; 1 : 0 ; x ± 7 : What is the PMF of X ? Give your reasoning. 3. Suppose X has the following PMF f X ( x ) = 8 > > > > > > < > > > > > > : 0 : 41 ; x = 0 ; 0 : 37 ; ; x = 1 ; 0 : 16 ; x = 2 ; 0 : 05 ; x = 3 ; 0 : 01 ; x = 4 : Find its CDF F X ( x ) : 4. For each of the following, determine the value of c that makes f ( x ) a PDF. (1) f ( x ) = c sin x; 0 < x < 2 ; (2) f ( x ) = ce x j ; ²1 < x < 1 : 5. Suppose f ( x ) = c [1 + 2 sin( x )]
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Unformatted text preview: for &amp; &lt; x &lt; &amp; and f ( x ) = 0 otherwise. Can you &amp;nd a value of c so that f ( x ) is a valid PDF. If yes, &amp;nd the value of c: If not, give your reasoning. 6. Let X have PDF f X ( x ) = 2 9 ( x + 1) ; 1 &amp; x &amp; 2 . Find the CDF F X ( x ) : 7. Suppose X has the geometric PMF f X ( x ) = 1 3 ( 2 3 ) x ; x = 0 ; 1 ; 2 ; ::: . Determine the PMF of Y = X= ( X + 1) . Note that here both X and Y are discrete random variables. 1...
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