term test 2 cheat sheet.docx - UNIT FOUR Permutations...

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UNIT FOUR: Permutations: selection matters, ex. First place for a prize. Combinations: order does not matter, ex. 5 spots within 20 applicants. Discrete random variable: takes on a countable number of possible values. Continuous random variables: takes on an infinite number of possible values. Expected value: E(x) or μ is the theoretical mean of a random variable, the expected value is the parameter E(x) = Σ(x) x P(x). Variance is the average squared distance from the mean: Var(x) = Σ(x- μ)² P(x). Var[x] = E[x²] – (E[x])². Standard deviation(x) = √Var(x). Some discrete random variables take on a countably infinite number of possible values, some discrete random variables take on negative values and have negative means, the standard deviation of a discrete random variable cannot be negative, the mean may be greater than, less than or equal to the standard deviation. Bernoulli Distribution: x is the outcome of a one-trial experiment, it’s either a success (x=1) of failure (x=0), x is the number of successes , P(X=x) = p x (1-p) (1-x) , E(x) = μ = p. Var(X) = σ² = p(1-p). Binomial Distribution: there is a fixed number of n trials, they’re independent, success (p) or failure (1-p) and the probability remains constant for all n trials, P(X=x) = (n/x) p x (1-p) (n-x) . E(X) = μ = np, Var(X) = σ² = np(1-p). The variance (np(1-p)) must be less than or equal to the mean (np), a binomial random variable represents a count and its value must be at least 0, the mean and variance of a binomial random variable has to be positive, it’s also a discrete random variable, the mean of a binomial random variable is np, the SD of a binomial random variable is √np(1-p) and for any given n, the variance of a binomial random variable is greatest when p=0.5, since p(1-p) is greatest when p=0.5 UNIT FIVE: Continuous distribution: f(x) is the height of the curve at the point x, f(x) ≥ 0 [always above the x axis], the total
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