Econ Sheet Exam 2

Econ Sheet Exam 2 - Probability of an event is its long-run...

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Probability of an event is its long-run relative frequency ; Must be legitimate 0 ≤ P ≤ 1 & sum of set of P’s = 1 Event – combination of outcomes For any random phenomenon, each attempt (or trial ) generates an outcome ( Discrete – distinct values / Continuous – some range) Something Has to Happen Rule ” – the probability of the set of all possible outcomes of a trial = 1 P(S) = 1 S is set of all possible outcomes Independent - Formal Def - Events independent if P (B|A) = P(B) prob of independent events don’t change when you find out one of them has occurred * No such thing as “law of averages” (promises short-run compensation for recent deviations from expected behavior) Law of Large Numbers –long-run relative frequency of repeated independent events gets closer to true relative frequency as number of trials increases Disjoint ( Mutually Exclusive ) – events that can’t occur together; no outcomes in common Complement Rule – The probability of an event occurring is 1 minus the probability that it doesn’t occur P(A) = 1 – P (A C ) Multiplication Rule – for INDEPENDENT events A & B “Some” means at least one complement of this is none; so P(at least one A in 5 trials) [ P(A) = .35 / P (A C ) = .65; P(none) in all 5 = (.65) ^ 5 Complement = 1 – ((.65) ^5) Sample Space – collection of all possible outcomes (which don’t have to be equally likely); Ex. If pulling bills from wallet S = {1, 5, 10, 20, 50, 100} General Addition Rule – DO NOT need disjoint events; General Multiplication Rule – DO NOT need independence; P( A and B) = P (A) * P(B |A) OR P(B) * P(A|B) Conditional Probability – P ( B | A) = “prob of B given A” * Mutually Exclusive events CANNOT be Independent Venn Diagram : Tree Diagram : Drawing w/o replacement – denominator changes because one less available each drawing; Ex: drawing something randomly like rooms ** P(B|A) ≠ P(A|B) [Baye’s Rule reverses conditional probs] Model for Distribution of Sample Proportions How a statistic (phat, b1, ybar) is distributed, NOT how data (p , μ, β) is distributed - Randomization leads to sample-to-sample variation creates sampling distribution for samples of particular size n -Distribution is N (p, √(p*q / n)) Normal model centered at true p with SD of √(p*q / n); Claim is more true as n grows… Assumptions : 1) Sampled values independent of each other 2) Sample size (n must be large enough) Conditions : 1)10 % Condition – sample size, n, must be no larger than 10% of population (if sample made w/o replacement) 2) Success/Failure Condition – the number of successes (n*p) and number of failures (n*q) must both be greater than 10 Central Limit Theorem –the sampling distribution model of the sample mean & proportion is approximately Normal for large n,
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Econ Sheet Exam 2 - Probability of an event is its long-run...

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