20082ee131A_1_HW5

# 20082ee131A_1_HW5 - EE 131A Homework#5 Due May 7th Read...

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

EE 131A Homework #5 Spring 2008 Due May 7th K. Yao Read Leon-Garcia (3rd edition), pp. 148-180. 1. If the probability of hitting a target is 0.2 and ten shots are ﬁred independently, what is the probability that the target will be hit at least once? At least twice? 2. Consider the close relationship between exponential waiting time and Poisson num- ber of arrivals. Assume the arrivals are independent. Let λ be the arrival rate (i.e., average number of arrivals per unit time). Let X be the waiting time for the next arrival (i.e., the waiting time between arrivals.) Assume the average number of arrivals in x unit time, denoted by λx, be Poissonly distributed. Denote F X ( x ) to be the cdf of X. Clearly, X 0 , since the waiting time can not be negative. Thus, F X ( x ) = 0 for x 0 . For 0 x, F X ( x ) = P ( X x ) = 1 - P ( X > x ) . But P ( X > x ) = P (noarrivalsin x unittime) . But λx is Poissonly distributed. Thus, P (noarrivalin xunit time) = exp( - λ x)( λ x) 0 / (0!) = exp(

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.

{[ snackBarMessage ]}

### Page1 / 2

20082ee131A_1_HW5 - EE 131A Homework#5 Due May 7th Read...

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

View Full Document
Ask a homework question - tutors are online