Unformatted text preview: 2 / 9 ? 6.3. Consider f ( x ) = c (1x 2 ) for1 < x < 1 and 0 otherwise. What value of c should we take to make f a density function? 6.4. Suppose X has density function x2 / 3 / 21 for 1 < x < 8 and 0 otherwise. Find EX , E ( X 2 ), and var( X ). 6.5. Suppose X has density function F ( x ) = x/ 2 for 0 < x < 2 and 0 otherwise. Find P ( X < 1) and P ( X > 3 / 2). 6.6. Suppose X has density function f ( x ) = 4 x 3 for 0 < x < 1 and 0 otherwise. Find (a) the distribution function F ( x ) = P ( X ≤ x ), (b) P ( X < 1 / 2), and (c) P (1 / 3 < X < 2 / 3)....
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 Fall '08
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 Math, density function, Texas A&M University Department of Mathematics Volodymyr Nekrashevych, Mathematics Volodymyr Nekrashevych

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