hw05 - Given B = (exactly) three successes have occurred in...

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ENEE 324 ASSIGNMENT 5 Due Tue 09/22 Problem 5A In the diagram below, information flows from the transmitter T to receivers R 1 and R 2 via links controlled by switches 1–6. Switches operate independently of each other, and the probability that a given switch is closed equals p . Let S i ( i = 1 ,..., 6) be the event that switch i is closed, and A j ( j = 1 , 2) be the event that there is a connection between T and R j . T R 2 R 1 1 2 3 4 5 6 Express your answers below in terms of fully expanded polynomials in p . (i) (3 pts.) Determine P [ A 1 ]. (ii) (3 pts.) Determine P [ A 2 ]. (iii) (3 pts.) Determine P [ A 1 A 2 ]. (iv) (2 pts.) Are A 1 and A 2 independent? (v) (3 pts.) Determine P [ A 1 A 2 ]. (vi) (3 pts.) Determine P [ A 1 | S 1 ]. (vii) (3 pts.) Does P [ S 1 S 2 | A j ] depend on whether j = 1 or j = 2? Explain. Problem 5B Consider a sequence of independent binary trials, each having success probability p = 3 / 5. (i) (2 pts.) What is the probability of A = “(exactly) six successes in ten trials”? (ii) (3 pts.)
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Unformatted text preview: Given B = (exactly) three successes have occurred in the rst four trials, what is the conditional probability of A ? (iii) (3 pts.) Determine P [ B | A ], expressing your answer as a ratio of two integers. (iv) (2 pts.) Show that the same result is obtained in (iii) above for any value p other than 0 or 1. Why is this so? (v) (4 pts.) By direct computation (using your calculator or MATLAB), determine the smallest value of n such that the probability of six or more successes in n trials exceeds 95%. (vi) (2 pts.) What is the probability of C = rst success occurs in the fth trial? (vii) (4 pts.) What is the probability of D = rst success occurs in (one of) the rst ve trials, and the second success occurs in (one of) the next ve trials?...
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This note was uploaded on 03/21/2010 for the course ENEE 324 taught by Professor Ephrimedes during the Fall '05 term at Maryland.

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