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# HW_4 - Soultions for Homework#4 3 a b Since pdf is...

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Unformatted text preview: Soultions for Homework #4 3. a. b. Since pdf is symmetric about 0, the answer is 0.5. c. 1 2 1 3 1 1 ( 1 1) 0. 09375( 4 ) 0. 09375[ 4 / 3] 0. 09375( 22 / 3) 0. 6875 P X x dx x x--- < < =- =- = = ∫ d. 0. 5 2 2 ( 0. 5 or 0. 5) 2 ( 0. 5) ( 0. 5) 0. 09375( 4 ) 0. 3164 P X X P X P X x dx-- < - = < - < - =- = ∫ Thus the answer is 2(0.3164)=0.6328 4. a. (1) pdf is nonnegative for all x. (2) 2 2 2 2 / ( 2 ) / ( 2 ) 2 [ ] 1 x x x e dx e θ θ θ ∞-- ∞ =- = ∫ c. 2 2 2 2 200 / ( 2( 100) ) / ( 2( 100) ) 200 100 2 100 [ ] 0. 471 100 x x x e dx e-- =- = ∫ d. 2 2 2 2 2 2 / ( 2 ) / ( 2 ) / ( 2 ) 2 ( ) [ ] 1 x y y x x y P X x e dy e e θ θ θ θ--- ≤ = =- =- ∫ Thus the expression for the distribution function is 2 2 / ( 2 ) ( ) 1 x x P X x e x θ- < ≤ = - ≥ 11. a. 1/4=0.25 b. 2 1 / 4 ( 0. 5) / 4 3 / 16 0. 1875- = = c. 1-P(X<0.5)=1-1/16=15/16 d. Since ( 2) 0. 5 F = . The answer is 2 e....
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HW_4 - Soultions for Homework#4 3 a b Since pdf is...

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