Practice quiz4 and soln - x ∞ ∞-∞-∞ = =...

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preQuiz 4 AMS310 Quiz will be on Monday October 13 ____1. Suppose f(x) = 1/6 for 0< X<6 and f(x) = 0 otherwise. Find the mean value of x. Suppose that Z has standard normal density (Z~N(0,1)). The p.d.f. of Z is f(z) = 2 / 2 2 1 x e - π for < < - x . Use Table 3 for the Standard Normal Distribution Function to answer Questions 2 through 4 below. _____ 2. P(Z< -1.65) = _____3. P( Z > 2.58) =____ _____ 4. z 0.025 = i.e., Find c such that P(Z> c) = 0.025. preQuiz 4 SOLUTIONS __ 3___ 1. Suppose f(x) = 1/6 for 0< X<6 and f(x) = 0 otherwise. Find the mean value of
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Unformatted text preview: x. . ∫ ∫ ∫ ∫ ∞ ∞-∞-∞ + = + + = = 6 6 6 ) 6 / 1 ( ) ( xdx dx x xdx dx x xf μ (x 2 /12) = 36/ 12 = 3.0 _ 0.05____ 2. P(Z< -1.65) = from the Table 3: Φ (-1.65)= 0.05 _ 0.005 ____3. P( Z > 2.58) =____ P(Z > 2.58) = 1- P(Z< 2.58) = 1- Φ (2.58) = 1- 0.995 = 0.005 (from Table 3: Φ (2.58)=F(2.58)=0.995) __ 1.96 ___ 4. z 0.025 = i.e., Find c such that P(Z> c) = 0.025. P(Z > z 0.025 ) = 0.025. So P(Z< z 0.025 ) = 0.975 and Φ (z 0.025 )=0.975. From Table 3: Φ (1.96)= 0.975 . So z 0.025 =1.96...
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