Econ171-Spring2010-02-Prob1-handout

Econ171-Spring2010-02-Prob1-handout - Economics 171 171...

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Economics 171 Decisions Under Uncertainty . Preliminary Concepts in 2. Preliminary Concepts in Probability Theory pring 2010 Spring 2010 Herb Newhouse 1 OSD: Review Example FOSD: Review Example 0 5; $100 0 5 $1 0 75; $2 0 25 B      $0,0.5; $100,0,5 , $1,0.75; $2,0.25 hat does FOSD say about and ? AB B What does FOSD say about 00 0 1 x x  0.5 0 100, 0.75 1 2 1 100 1 2 Fx F x xx       When 0.5, 0.5 0 cannot FOSD . x FF A B When 15, 0.5 1 cannot FOSD . A B x B A 2 eadings Readings achina Reader Machina Reader – Handout 2: p. 8 - 13 • Lindley – Ch. 2: 2.1 – 2.8, 2.13 – Ch. 3: 3.1 – 3.3, 3.5 – 3.10, 3.12, 3.14, 3.16 3 utline Outline robability distributions and cumulative Probability distributions and cumulative distribution functions. xpected value variance and other • Expected value, variance and other descriptors. • Concave functions and convex functions. 4
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Probability Distributions Discrete probability distribution: random variable can take on differen values i  A random variable can take on different values. 01 i Xi PX x  1 Example: Suppose you flip a coin twice. i i p  What are the possible outcomes? ,,, TT TH HT HH Let be the total n X umber of heads. What's the probability of a given ? 2 1 X 12 0, 1, 2 44 4 pX  5 ontinuous probability distribution: Continuous probability distribution: A random variable can take on any value in a range. 1 b X a X b f xd x      1 a Pa X b fxd x   Example: The high temperature for tomorrow. It's equally likely to be anything betwee n 74 and 76. 11 x         75 75 76 74 2 1 1 1 74 75 75 74 fx p Xd x x          74 74 22 2 2 2   6 umulative Distribution Functions Cumulative Distribution Functions The cumulative distribution function (CDF) is the probability that the random variable takes a value less than or equal to . X x Discrete:     0 x i Fx pX i Continuous: x x f d      7 umulative Distribution Functions Cumulative Distribution Functions iscrete: Number of heads given two flip Discrete: Number of heads given two flips. x 0 0 for 0 1 0 1 i x for 4 for 1 2 x x   42 111 + for 2 24 x  424 8
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DF Number of Heads CDF Number of Heads 1 /4 3/4 1/4 0 1 2 #Heads 9 umulative Distribution Functions Cumulative Distribution Functions
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This note was uploaded on 10/21/2010 for the course ECON 809880 taught by Professor Herbnewhouse during the Spring '09 term at UCSD.

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Econ171-Spring2010-02-Prob1-handout - Economics 171 171...

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