assignment_2_08

assignment_2_08 - ESO 209 PROBABILITY STATISTICS Semester 2...

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ESO 209: PROBABILITY & STATISTICS Semester 2: 2007-08 Assignment #2 Instructor: Amit Mitra [1] For events , A B and C such that ( ) 0, PC > prove that (a) () ( ) ( ) ( ) ||| PA BC PAC PBC PABC =+− | (b) ( ) |1 | C PA C =− . [2] Let A and B be two events such that ( ) 0 PA 1 < < . Which of the following statements are true? (a) ( ) || C PAB PA B += 1 (b) ( ) C 1 (c) ( ) CC 1 [3] Consider the two events A and B such that ( ) 14, = ( ) PBA = 2 and = 4 . Which of the following statements are true? (a) A and B are mutually exclusive events, (b) A B , (c) ( ) |3 = 4 , (d) ( ) C 1 [4] Consider an urn in which 4 balls have been placed by the following scheme. A fair coin is tossed, if the coin comes up heads, a white ball is placed in the urn otherwise a red ball is placed in the urn. (a) What is the probability that the urn will contain exactly 3 white balls? (b) What is the probability that the urn will contain exactly 3 white balls, given that the first ball placed in the urn was white? [5] A random experiment has three possible outcomes, A , B and C , with probabilities A p , and .
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This note was uploaded on 08/19/2009 for the course EE EE210 taught by Professor J.john during the Spring '08 term at IIT Kanpur.

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assignment_2_08 - ESO 209 PROBABILITY STATISTICS Semester 2...

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