COMPSCI 70 Chapter Notes - Chapter 19: Discrete Uniform Distribution, Bernoulli Distribution, Geometric Distribution
31 Jan 2018
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Bernoulli distribution bernouli distribution - describes a random variable that only takes on the values ; distribution for a indicator random variable. The probability that in trials, there are successes is. A random variable with a binomial distribution: , where is the probability of a single trial and is the number of values can take on. By the linearity of expectation and knowing that there are trials, we get. Method: using linearity of variance and independent bernoulli random variables is. To find , we can add the variances of each , because are independent. Note that for indicator random variables (see more in variances notes) From the calculations of expectation above, we see that the expectation of the indicator variables. Derivation: https://math. stackexchange. com/questions/849196/distribution -of-a-binomial-variable-squared (discrete) uniform distribution - a distribution used when the random variable is equally likely to take any of the values in its range (" is uniformly distributed in its range")
