HW1sol

# HW1sol - B ) c ] = 1-. 8 = 0 . 2 1.4.2: Pick a light bulb...

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STAT516 Solution to Homework 1 1 1.1.4: We have 18 black, 18 red, 2 green, total 38 a) P(both lose)=2/38 b) P(at least one wins)=1-P(both lose)=36/38 c) P(at least one loses)=1-P(both win)=1-0=1 1.3.2: a)( AB c ) ( A c B ) or A B - AB b)( A B C ) c or A c B c C c c)Exactly one: ( AB c C c ) ( A c BC c ) ( A c B c C ) or A B C - AB - BC - AC Exactly two: ( ABC c ) ( AB c C ) ( A c BC ) or ( AB ) ( BC ) ( AC ) - ABC Three: ABC 1.3.4: a)Yes: { 0 , 1 } b)Yes: { 1 } c)No. This is a subset of the event { 1 } but it is not identical to { 1 } , because the event(ﬁrst toss tails, second toss heads) also is a subset of { 1 } . d)Yes: { 1 , 2 } 1.3.5: a) ﬁrst coin lands heads b) second coin lands tails c) same as a) d) at least two heads

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STAT516 Solution to Homework 1 2 e) exactly two tails f) ﬁrst two coins land the same way. 1.3.8: a) P ( A B ) = P ( A ) + P ( B ) - P ( AB ) = 0 . 6 + 0 . 4 - 0 . 2 = 0 . 8 b) P ( A c ) = 1 - P ( A ) = 0 . 4 c)similarly P ( B c ) = 0 . 6 d) P ( A c B ) = P ( B ) - P ( AB ) = 0 . 4 - 0 . 2 = 0 . 2 e) P ( A B c ) = P [( A c B ) c ] = 1 - 0 . 2 = 0 . 8 f) P ( A c B c ) = P [( A
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Unformatted text preview: B ) c ] = 1-. 8 = 0 . 2 1.4.2: Pick a light bulb at random. Let D be the event (the light bulb is defective), and B be the event ( the light bulb is made in city B). Then P ( B ) = 1 / 3 ,P ( D | B ) = . 01, and P ( D c B ) = P ( D c | B ) P ( B ) = [1-P ( D | B )] P ( B ) = 0 . 99 × 1 / 3 = 0 . 33 1.4.3: P ( rain tomorrow | rain today ) = P ( rain today and tomorrow ) P ( rain today ) = . 3 . 4 = 3 / 4 1.4.4: Call the events A(having probability 0.1) and B(having probability 0.3). a) P ( A c B c ) = P ( A c B c ) = 0 . 9 × . 7 = 0 . 63 b) 1-P ( A c B c ) = 0 . 37 c) P ( AB c ∪ A c B ) = P ( AB c ) + P ( A c B ) = 0 . 1 × . 7 + 0 . 9 × . 3 = 0 . 34...
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## This note was uploaded on 09/14/2009 for the course STAT 134 taught by Professor Aldous during the Fall '03 term at Berkeley.

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HW1sol - B ) c ] = 1-. 8 = 0 . 2 1.4.2: Pick a light bulb...

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