Homework 3 - number of signals the machine receives. Let...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 116 Homework 3 Due Wednesday, April 23th. Please show work and justify answers. No credit for a final answer with no explanation, even if the answer is correct. 1. Airlines find that each passenger who books a flight fails to check-in with probability 1 10 independently of the other passengers. So airline A decides to sell 10 tickets for their 9 seat plane while airline B decides to sell 20 tickets for their 18 seat plane. Which airline is more often overbooked? 2. Let ξ be the times of throwing a dice until every possible numbers 1,2,3,4,5,6 appear at least once. Calculate E [ ξ ]. 3. A machine receives signals and the number of signals it receives has a poisson( λ ) distribution. The signal is either positive or negative and the probability for the signal to be positive is p. Signals are mutually independent and are independent of the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: number of signals the machine receives. Let the number of positive signals it receives be η and find the distribution of η . 4. Put n balls randomly into m boxes, ξ is the number of empty boxes. Calculate E [ ξ ]. 5. Ross Page 195, problem 65 6. Ross Page 200, problem 27 7. The Pareto distribution, with parameters α and β , has probability density function f ( x ) = α β β x β +1 ,α < x < ∞ ,α > ,β > a) Verify that f ( x ) is a probability density function b) Derive the mean and variance, and specify the conditions we must impose on β in order for the mean and variance to be finite. 8. Random variable X has a probability density f ( x ) = 1 2 x + 3 4 , ≤ x ≤ 1 and f ( x ) = 0 elsewhere. Calculate P (( | 2 X 3-35 216 | > 19 216 ) ∩ ( X 2 < 9 16 )). 1...
View Full Document

This note was uploaded on 01/13/2010 for the course STATS 116 taught by Professor Staff during the Spring '07 term at Stanford.

Ask a homework question - tutors are online