{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quiz4Aans - STAT 408 Spring 2009 Version A Name ANSWERS...

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

View Full Document Right Arrow Icon
STAT 408 Spring 2009 Version A Name ANSWERS . Section __________ Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Suppose that number of accidents at the Monstropolis power plant follows the Poisson process with the average rate of 0.40 accidents per week. Notations: X t = number of accidents in t weeks. T k = time of the k th accident. a) (3) Find the probability that the first accident would occur during the fourth week. T 1 has Exponential distribution with λ = 0.40 or θ = 1 / 0.4 = 2.5. P ( 3 < T 1 < 4 ) = - 4 3 4 . 0 4 . 0 dt t e = e 1.2 e 1.6 0.0993 . OR P ( 3 < T 1 < 4 ) = P ( T 1 > 3 ) – P ( T 1 > 4 ) = P ( X 3 = 0 ) – P ( X 4 = 0 ) = P ( Poisson ( 1.2 ) = 0 ) – P ( Poisson ( 1.6 ) = 0 ) = 0.301 – 0.202 = 0.099 . OR k fourth wee the during accident one least at weeks e first thre the during accidents no P AND = P ( X 3 = 0 ) × P ( X 1 1 ) = 0.301 × ( 1 – 0.670 ) 0.0993 . OR Week 1 Week 2 Week 3 Week 4 no accident no accident no accident accident(s) 0.670 × 0.670 × 0.670 × 0.330 0.0993 .
Image of page 1

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

View Full Document Right Arrow Icon
b) (4) Find the probability that the third accident would occur during the fifth week.
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}