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Unformatted text preview: n . Find F Y n ( y ) = P ( Y n ≤ y ), – ∞ < y < ∞ . F Y n ( y ) = P ( Y n ≤ y ) = ( F ( y ) ) n = & & ± & & ² ³ < ≥ ´ ´ µ ¶ · · ¸ ¹2 2 2 1 y y y n c) (3) Let n n n Y Z = . Find F n ( z ) = P ( Z n ≤ z ), – ∞ < z < ∞ . F n ( z ) = P ( Z n ≤ z ) = P ( Y n ≤ n z ) = & & ± & & ² ³ < ≥ ´ µ ¶ · ¸ ¹n z n z z n n 2 2 2 1 d) (3) Find the limiting distribution of Z n . That is, determine the cumulative distribution function F ∞ ( z ) = ∞ → n lim F n ( z ), – ∞ < z < ∞ . ( You probably have not seen this cumulative distribution function before. ) F ∞ ( z ) = ∞ → n lim F n ( z ) = & & ± & & ² ³ ≤ >2 z z e z...
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This test prep was uploaded on 04/13/2008 for the course STAT 410 taught by Professor Alexeistepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 AlexeiStepanov
 Probability

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