quizexe3 - x > 3, F ( x ) = 1. For-3 x 3 F ( x )...

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STAT 427 Quiz/Class Exercise 3: With Solution Suppose that the p.d.f. of a random variable X is as follows: f ( x ) = ( c (9 - x 2 ) - 3 x 3 0 otherwise (a) Determine the value of the constant c . (b) What is P r ( - 1 X 1)? (c) Construct the c.d.f. (d) What is P r ( X < 0). (a) 1 = Z 3 - 3 c (9 - x 2 ) dx = c Z 3 - 3 (9 - x 2 ) dx = c (9 x - x 3 3 ) ± ± ± ± ± 3 - 3 = 36 c, c = 1 36 . (b) P ( - 1 X 1) = Z 1 - 1 1 36 (9 - x 2 ) dx = 13 27 . (c) For x < - 3, F ( x ) = 0, for
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Unformatted text preview: x &gt; 3, F ( x ) = 1. For-3 x 3 F ( x ) = P ( X x ) = Z x-3 1 36 (9-y 2 ) dy =-1 108 x 3 + 1 4 x + 1 2 Therefore, F ( x ) = x &lt;-3-1 108 x 3 + 1 4 x + 1 2-3 x 3 1 x &gt; 3 (d) P ( X &lt; 0) = F (0) = 1 2 . 1...
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