Section_1_Note_v1

Section_1_Note_v1 - Section 1 - Econ 140 GSI: Hedvig,...

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Unformatted text preview: Section 1 - Econ 140 GSI: Hedvig, Tarso, Xiaoyu * 1 Review 1.1 Summation Operator De nition : N i =1 X i = X 1 + X 2 + ... + X N Rules : 1. N i =1 kX i = k N i =1 X i 2. N i =1 ( X i + Y i ) = N i =1 X i + N i =1 Y i 3. N i =1 k = kN 4. X = 1 N N i =1 X i 5. N i =1 ( X i- X ) = 0 6. N i =1 N j =1 X i Y j = N i =1 X i N j =1 Y i ! 7. N i =1 N j =1 ( X ij + Y ij ) = N i =1 N j =1 X ij + N i =1 N j =1 Y ij 1.2 Random Variable De nition : A random variable captures randomness in life. It is the numerical representation of random events. It is a variable that takes alternative values, each with a probability less than or equal to 1 and larger or equal to 0. Types of random variable : Discrete : takes only a nite (more precisely: countable) number of values on the real line Continuous : takes a continuum of values on the real line Probability distribution : process that generates the values of a random variable. For a discrete random variable it lists all possible outcomes of the random variable with their associated probabilities [ P ( X = x )] * Thanks for previous GSI Edson Severnini sharing his section notes. 1 For a continuous random variable it can be described by the probability density function (p.d.f.) . The area under the p.d.f. between any two points is the probability that the random variable falls between those two points (SW p.18) Both discrete and continuous random variables can be described by the Cumulative distribution function (c.d.f.) , which cumulates the total probability until a certain value of the random variable: F ( x ) = P ( X x ) Also, probability distributions are often summarized or described in terms of their means and variances, which in their turn are de ned in terms of the expectation operator E ....
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Section_1_Note_v1 - Section 1 - Econ 140 GSI: Hedvig,...

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