# PS04 - q=0.1.What is the minimum value of k in order to...

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

ECSE4500 P.S.#4 Due 10/2/2008 (1) (20 points) The number of buses that arrive at a bus stop in T minutes is a Poisson random variable, B , with parameter α = T/5 . (a) (5 points) What is the PMF of B , the number of buses that arrive in T minutes? (b) (5 points) What is the probability that in a two minute interval, three buses will arrive? (c) (5 points) What is the probability of no buses arriving in a 10-minute interval? (d) (5 points) How much time should you allow so that with probability 0.99 at least one bus arrives? (2) (10 points) A particular circuit works if all of its component devices work. There are 10 component devices in each circuit. Each component device costs \$2 . Each circuit is tested before leaving the factory. Each working circuit can be sold for k dollars, but each non- working circuit is worthless and must be thrown away. Each device has a failure probability
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: q=0.1 .What is the minimum value of k in order to have an expected profit of \$1 per manufactured circuit? (3) (20 points) The CDF of a continuous random variable X is ⎪ ⎩ ⎪ ⎨ ⎧ ≥ < ≤ − + − < = 1 1 1 1 2 / ) 1 ( 1 ) ( x x x x x F X Find (a) (8 point) ) ( x f X (b) (6 point) ] [ X E (c) (6 point) ] [ X VAR (4) (30 points) A continuous random variable X has PDF ⎩ ⎨ ⎧ ≤ ≤ − = otherwise x x f X 3 1 4 / 1 ) ( Define the random variable Y by Y=h(X)=X 2 . Find (a) (5 points) E[X] (b) (5 points) VAR[X] (c) (5 points) h(E[X]) (d) (5 points) E[h(X)] (e) (5 points) E[Y] (f) (5 points) VAR[Y] (5) (20 points) The PDF of a random variable X is ⎩ ⎨ ⎧ ≥ = − otherwise x e x f x X ) 2 / 1 ( ) ( 2 / Find a. (5 points) ] 2 1 [ ≤ ≤ X P b. (5 points) F X (x) c. (5 points) E[X] d. (5 points) VAR[X]...
View Full Document

## This note was uploaded on 10/19/2008 for the course ECSE 4500 taught by Professor Woods during the Fall '08 term at Rensselaer Polytechnic Institute.

Ask a homework question - tutors are online