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Additive Law |
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Bayes' Theorem |
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Beta Distribution |
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| •Values between 0 and 1
•Percentages are often beta distributed |
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Binomial Distribution |
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| •Discrete Random Variable
•Fixed number of trials
•2 outcomes in each trial
•p=Probability of success
•q=Probability of failure
•trials are independent (p+q don’t change from trial to trial)
•random variable y = number of successes
example is p of getting 5 questions on 8 question exam by guessing- 5 choices
y=5 n=8 p=1/5 q=4/5 |
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cdf |
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Chi Squared Distribution |
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| Special type of gamma distribution |
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Conditional Probability |
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Covariance |
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Derivatives |
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| rate of change of a function = slope |
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Distributive Laws of Probability |
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Gamma Distribution |
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| •Continuous Random Distribution
•Used for non-negative events skewed to the right
•Parameters are alpha and beta
•Alpha is the scale beta is the shape |
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Geometric Distribution |
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| •Discrete Random Variable
•Independent Trials
•Asks when the first success (or failure) will occur
•Example- guy has 1% chance of winning election p=.01 q=.99 |
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Hypergeometric Distribution |
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| •Discrete Random Variable
•proportion changes as we sample
•example- 20 phds – pick 10 what is p of picking 5 best N=20 n=10 r=5 y is subset of r that you want – in this case 5 |
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Integration |
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| Inverse of derivative |
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Linear Regression |
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Multiplicative Law |
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nCr |
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Negative Binomial Distribution |
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| •Discrete Random Variable
•Know xth success happens on nth trial
•r = event of interest
•example – p of stringing oil on 3rd oil strike on 5th try (p of oil is .2) y=5 r=3 p=.2 q=.8 |
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nPr |
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pdf |
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Pearson's r |
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Poisson Distribution |
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| •Discrete Random Variable
•interested in counts- number of times something happens
•The number of occurances in any two subintervals must be independent
•Probability of an occurance in any short time interval must be approximately proportional to the length of time interval
•Subintervals where only one event can happen
•Lambda = number of trials, x probability of success
•Example number of bills reported in a session (25 is the historical average) reported by a committee in congress- what is probability of them reporting only 10? y=10 lambda=25 |
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Rules for Independence |
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Spearman Rho |
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Standard Deviation |
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Standard Error of OLS Reg. Estimate |
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Uniform Distribution |
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| •Continuous Random Distribution
•For any point, the probability distribution is the same
•All points are equally likely
•It is flat – uninformative
•theta 1 and 2 are parameters for distribution
•Example- bills reported sometime over 10 hours – what is p of between hours 9 and 10? Theta1 = 0 theta2 = 10… integrate between 9 and 10 dx=(1/10)y so (y/10)-(y/9)=1/10 chance of bills reported in between 9 and 10 |
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Variance |
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Variance of OLS Regression Error |
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Z-Score |
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