131A_1_Lecture15-1_Winter_2012

131A_1_Lecture15-1_Winter_2012 - EE 131A Probability...

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UCLA EE131A (KY) 1 EE 131A Probability Professor Kung Yao Electrical Engineering Department University of California, Los Angeles Lecture 15-1
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UCLA EE131A (KY) 2 MC Simulations (1) Ex. 1. Suppose we toss a “fair” coin 100 times. At each toss, if we have a head, we receive a dollar and if we have a tail, we lose a dollar. Assume we start with $10. Here are the simulations of four realizations.
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UCLA EE131A (KY) 3 MC Simulations (2) Ex. 1 (Continue). After 100 tosses, in realizations #1 and #3, we have more than $10 (and thus we are winning). In realization #4, we have less than $10 (and thus we are losing). In realization #2, around toss 70, we had 0 dollar. In practice, if we have no more money to play, then we had to stop. However, if we are allowed to continue (such as if our credit is good), then we actually recover with some positive dollars, but ended up with 0 dollar again around toss 75.
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UCLA EE131A (KY) 4 MC Simulations (3) Ex. 1 (Continue). If we continue (such as if our credit is good), then we went positive again, but went to 0 dollar around toss 89 and continue into the negative region, until around toss 96 or so. By toss 100, we ended up with about $4. The purpose of these four realizations shows that even with a “fair coin” (in which each outcome is theoretically equal to be up $1 as down $1), the long term effects (after say 100 tosses) in these four
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This note was uploaded on 02/29/2012 for the course ELECTRICAL 131a taught by Professor Yao during the Spring '12 term at UCLA.

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131A_1_Lecture15-1_Winter_2012 - EE 131A Probability...

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