# 8 - ECMT 1020 Summer School 09 Lecture 8 Random Variables and Portfolio Analysis Discrete Probability Distribution Experiment Toss 2 Coins 4

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ECMT 1020 Summer School 09 Lecture 8- Random Variables and Portfolio Analysis

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Experiment: Toss 2 Coins. Let X = # heads. T T Discrete Probability Distribution 4 possible outcomes T T H H H H Probability Distribution 0 1 2 X X Value Probability 0 1/4 = 0.25 1 2/4 = 0.50 2 1/4 = 0.25 0.50 0.25 Probability
Discrete Random Variable Summary Measures Expected Value (or mean) of a discrete distribution (Weighted Average) Example: Toss 2 coins, X = # of heads , compute expected value of X: E(X) = (0 x 0.25) + (1 x 0.50) + (2 x 0.25) = 1.0 X P(X) 0 0.25 1 0.50 2 0.25 = = = μ N 1 i i i ) X ( P X E(X)

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Variance of a discrete random variable Standard Deviation of a discrete random variable where: E(X) = Expected value of the discrete random variable X X i = the i th outcome of X P(X i ) = Probability of the i th occurrence of X Discrete Random Variable Summary Measures = - = N 1 i i 2 i 2 ) P(X E(X)] [X σ (continued) = - = = N 1 i i 2 i 2 ) P(X E(X)] [X σ σ
Example:

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## This note was uploaded on 02/10/2012 for the course ECON 1002 taught by Professor Markmelatos during the Three '10 term at University of Sydney.

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8 - ECMT 1020 Summer School 09 Lecture 8 Random Variables and Portfolio Analysis Discrete Probability Distribution Experiment Toss 2 Coins 4

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