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Variance and Standard Deviation in Probability
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Geometric Random Variable (number of trials until first success, with success probability p)
Negative Binomial Random Variable (number of trials until r-th success)
Normal Random Variable (mean and variance )
Variance is given by parameter . Standard Deviation is
Discrete Random Variable with Finite Outcomes
Variance is the sum of the product of each outcome's probability and the square of its deviation from the mean.
Uniform Random Variable (continuous, with range to )
Chi-Squared Random Variable (sum of squares of k standard normal random variables)
Variance is where is the degrees of freedom. Standard Deviation
Multinomial Random Variable (n independent trials, each with k possible outcomes)
For any two outcomes and , if . For outcome , . Standard Deviation
Binomial Random Variable (n independent trials, each with success probability p)
Poisson Random Variable (events in fixed interval with mean rate )
Variance is equal to the mean rate .
Exponential Random Variable (time until event with rate )
Variance is given by .
Hypergeometric Random Variable (successes in samples without replacement)
Continuous Random Variable with Probability Density Function (PDF)
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