ISE361_HW4answers_F03

ISE361_HW4answers_F03 - Homework Four Fall 2003 2. F(x) = 1...

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Homework Four Fall 2003 2. F(x) = 1 / 10 for –5<= x <= 5, and =0 otherwise a) P(x<0) = (-5 to 0) 1/10 dx = .50 b) P(-2.5< x <2.5) = (-2.5 to 2.5) 1/10 dx = .50 c) P(-2<= x <=3) = (-2 to 3) 1/10 dx = .50 d) P(k< x < k+4) = (k to k+4) 1/10 dx = x/10| k k+4 = 1/10[(k=4)-k] = .40 4. a) 0 – (-1) = 1 2 2 d) 1 – e -x / 2( θ ) 10 b) θ k / θ k = 1 14. a) If X is uniformly distributed on the interval from A to B, then E(X)= Integral (AtoB) x/(B-A)dx = (A+B) / 2, E(X 2 ) = (A 2 +AB+B 2 )/ 3 V(X)= E(X 2 ) – [E(X)] 2 = (B-A) 2 / 2 Here A = 7.5 & B = 20; E(X) = 13.75, V(X) = 13.02 b) F(X) = (x-7.5) / 12.5 for (7.5<=x<=20) 1 for x =>20 c) P(X<=10) = F(10) = .200; P(10<=x<=15) = F(15) – F(10) = .40 d) SD = 3.61, so u +/- SD = (10.14, 17.36) Thus, P( u σ <= x <= u + σ ) = F(17.36) – F(10.14) = .5776 Similarly, P( u σ <= x <= u + σ ) = P(6.53<= x <=20.97) = 1.0 22. a) For (1<= x <=2); F(x) = (1tox) 2(1-1/x 2 )dx = 2(x+1/x)| x 1 = 2(x+1/x) – 4 so F(x) = 0 for x <1 =2(x+1/x) –4 for 1<= x <=2 =1 for x>2 c) E(X)= (1to2) x 2(1-1/x
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This homework help was uploaded on 04/16/2008 for the course ISE 361 taught by Professor Koon during the Spring '08 term at Binghamton.

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ISE361_HW4answers_F03 - Homework Four Fall 2003 2. F(x) = 1...

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