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Econ173A_topic0

Econ173A_topic0 - ^ Economics Economics NOTES Foster UCSD...

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^ α •• • •• • •• • •• • • •• •• x i y i Fig. 1 β ^ Economics REVIEW OF STATISTICS p. 1 Economics Courses STATISTICS NOTES Foster, UCSD 13:14:40 TOPIC 0 – REVIEW OF STATISTICS A. Random Variables and Probability 1. Population: a) In statistics application, we have some population of elements which we wish to des-cribe, explain or predict. b) Examples -- all Ec 17#A students; all common stocks on NYSE. 2. Statistical Experiment: a) A stochastic (random) process or experiment yields one of several or infinitely many possible outcomes e j each time it is performed. The set of possible outcomes is sample space S = {e j , j = 1...k}. b) The process is random because one never knows in advance which outcome will result. c) Example -- flip a coin: S = {e 1 = H, e 2 = T}. 3. Probability: a) Each outcome e j occurs with a given probability P j . b) If an experiment is repeated N times and e 2 occurs N 2 times, then P 2 = Pr(e 2 ) = Lim N 2 /N as N → . 4. Random Variable: a) A random variable is a function (say X) which assigns a real number x i , i = 1,2... (NOT a probability) to each outcome in the sample space of an experiment. b) Each repetition of the experiment yields an outcome e j and thus a value X = x i of the RV. c) Example -- if the experiment is flip a coin and X = number of heads, then the possible values are x 1 = 0, x 2 = 1.

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Economics REVIEW OF STATISTICS p. 2 5. Probability Distribution: a) Every RV X has distribution f(x). b) Discrete RVs have a finite number of possible values x i , i=1...m. Since each e j occurs with Pr(e j ), each x i also occurs with some probability. Probability distribution f(x i ) = Pr(X = x i ): 0 < f(x i ) < 1, i=1...m; Σ f(x 1 ) = 1.
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