Probability 26Feb2016.ppt - Applied Statistics • Probability – – – – • Probability Distribution – – – – – • Probability of

Probability 26Feb2016.ppt - Applied Statistics •...

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Applied Statistics Probability Probability of simple events Probability of compound events Probability using tree diagrams Bayes Theorem Probability Distribution Probability pattern of discrete variables Probability of continuous variables Mean and mode of continuous variables Binomial Distribution Poisson Distribution Regression Regression lines and their equations
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Probability, Set Operations What is probability? a branch of mathematical framework for reasoning about uncertainty Classical Interpretation : all outcomes have equal probability dice {1,2,3,4,5,6} P(1) = 1 / 6 , P(2) = 1 / 6 … Relative Frequency P(pin-UP) = 32 P(pin-Down) = 68 Subjective Interpretation (nature of problem): uses a model, randomness involved such as weather drop of paint falls into a glass of water, model can describe P(hit bottom before sides ), P(survival after surgery) -“subjective,” estimated by the doctor. Frequency Interpretation: probability based on history P(make a free shot) is based on history of shots made at basket.
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Probability for Equally Likely Outcomes
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UK lottery ball frequency UK lottery ball frequency 0 20 40 60 80 100 120 140 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
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500 1000 1500 2000 2500 3000 3500 4000 Heads Tails Counter intuity #1 Counter intuity #1 4000 flips of a Euro coin 4000 flips of a Euro coin lands on “heads” 2780 times (68%) lands on “heads” 2780 times (68%) evidence of an unfair coin? evidence of an unfair coin?
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Calculating Probabilities Calculating Probabilities Minesweeper Minesweeper clicking on a cell containing a mine clicking on a cell containing a mine ends the game ends the game clicking on a cell containing no mine, clicking on a cell containing no mine, but adjacent to but adjacent to x x mines,will reveal the mines,will reveal the number of conjoining mines number of conjoining mines clicking on a square containing no mine, clicking on a square containing no mine, and not adjacent to a mine, will reveal nothing and not adjacent to a mine, will reveal nothing
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What is the probability of our first move clicking on a cell containing a mine? 64 cells 10 mines 10 / 64 = 0.15625 15.6% or p = 0.156 What is the probability of clicking on a mine in the highlighted block? 8 cells 1 mine 1 / 8 = 0.125 12.5% or p = 0.12 What about the green block ? 8 cells 3 mines 3 / 8 = 0.375 p = 0.375 Calculating Probabilities Calculating Probabilities
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Roulette You plan to bet on number 13 on the next spin of a roulette wheel. What is the probability that you will lose? Solution A roulette wheel has 38 different slots, only one of which is the number 13. A roulette wheel is designed so that the 38 slots are equally likely. Among these 38 slots, there are 37 that result in a loss. Because the sample space includes equally likely outcomes, we use the classical approach (Rule 2) to get P (loss) = 37 38
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Lecture Goals Probabilistic models Sample space Which is basically a description of all the things that may happen during a random experiment.
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