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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online