STA261H1 Lecture Notes - Lecture 1: Sample Space, Linear Map, Indicator Function

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23 Feb 2019
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The probability measure p for each event a de ned on sample space satis es the following properties: P (a) is non-negative and 0 p (a) 1. P (a) = 0 when a is empty. P (a) = 1 when a is the entire sample space . Expected value/ mean/ average of random variable (x) is de ned as. Xf (x)dx when x is continuous or. E[x] = pi xip [x = xi] when x is discrete. X is the outcome of rolling a fair dice. Let x and y are two random variables and a, b and c are few constants. E[ax + by + c] = ae[x] + be[y ] + c. If a is any event, we can de ne the indicator function of a, written ia, to be the random variable for all s . Ia(s) = 1, if s a. Probability expressed as the expectation of indicator function.

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