that is not possible. Neither can the slope be positive, or else we would have y < 0, and again this is not possible, because probabilities must be between 0 and 1. Therefore the slope must be 0, or y ( x ) is constant, or y ( x ) = 1 for all x . In other words, one is certain to get to $200 eventually (provided, of course, that one is allowed to go into debt). There is nothing special about the ﬁgure 300. Another way of seeing this is to compute as above the probability of getting to 200 before-M and then letting M → ∞ . 4. Random variables. A random variable is a real-valued function on S . Random variables are usually denoted by X,Y,Z,. .. Example. If one rolls a die, let X denote the outcome (i.e., either 1,2,3,4,5,6). Example. If one rolls a die, let Y be 1 if an odd number is showing and 0 if an even number is showing. Example. If one tosses 10 coins, let X be the number of heads showing. Example.
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This note was uploaded on 12/29/2011 for the course MATH 317 taught by Professor Wen during the Spring '09 term at SUNY Stony Brook.