{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

section 4doc

# section 4doc - CEE 3040 Fall 2008 CEE 304 Section 4...

This preview shows pages 1–3. Sign up to view the full content.

CEE 3040 Fall 2008 CEE 304 – Section 4 Problems 1. Memoryless Exponential Process : ( ) x X f x e λ λ - = for x 0 ( ) 1 x X F x e λ - = - for x > 0 By definition: ( ) [ ] X F x P X x = [ ] 1 ( ) x X P X x F x e λ - = - = If we already waited t minutes, how much longer do we expect to wait? [i.e. What is the mean of the additional waiting time A ?] t t a X X A e e t F t a F t X P t X t a X P t X t a X P a F λ λ - + - = - + - = + = + = ) ( ) ( 1 ) ( 1 ] [ ] [ ] | [ ) ( a A e a F λ - = ) ( , for a > t Therefore, the distribution of the additional waiting time A is the same as the original waiting time T, it is just shifted over by t . So, E [ A ] = E [X | X t ] = t + 1/ λ . Doesn’t matter how long you have waited, the expected additional waiting time has mean 1/ λ . 2. An engineering student got a summer job setting off fireworks on the 4 th of July and other summer events. For a particular display, the bomb is shot from the tube so that after t seconds it is at height: H = (100 m/sec) t – 0.5 (10 m/sec 2 ) t 2 = 500 – 5(10 – t) 2 meters Unfortunately the timers on the bombs are not accurate. The student estimates that the timer will yield a time T to detonation after launch that is normally distributed with mean 10 seconds and standard deviation 1.2 seconds. T ~ N( μ = 10 sec, σ 2 = (1.2 sec) 2 ) a.) What is the probability that the bomb explodes more than 495 meters above the ground? ] 495 ) 10 ( 5 500 [ ] 495 [ 2 - - = t P H P = 0.5934 b.) Above what height can you be 99% confident the bomb will explode? 99 . 0 ] [ = h H P 99 . 0 ] ) 10 ( 5 500 [ 2 = - - h t P Ans . h = 452.26 m

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

View Full Document
CEE 3040 Fall 2008 c.) What is the pdf for the height at which the bomb explodes?
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 6

section 4doc - CEE 3040 Fall 2008 CEE 304 Section 4...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online