section4.1-4.2-students_SP11

section4.1-4.2-students_SP11 - Recap: Discrete...

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1 Recap: Discrete Distributions section 3.6 1 Hypergeometric () r N r x n x P X x N n              , max{0, ( )}, ,min{ , } x n N r n r 1 ( ) (1 ) 1 x r r x P X x p p r , x = r , r +1, … 2 ) ( ) ( ) r r p E X V X p p Negative Binomial ( ) , where / . ( ) 1 E X np p r N Var X fpc n p p   2 What is ahead: Continuous Distributions • Generic setup for continuous distributions: • Cumulative Distribution Function ( cdf ): F(x) = P(X ≤ x) • Probability Density Function ( pdf ) : f(x) “similar” to pmf • P (X ≤ b), P(X ≥ a), P(a ≤ X ≤ b), …. • Expectation : E[X] = μ • Variance : V(X) = E [ (X - μ) 2 ] • Specific Continuous Distribution • Uniform • Normal (Gaussian) • Gamma, Exponential, Chi-squared, …
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2 Continuous Random Variables Recall : X is a continuous random variable if the set of its possible values is an interval (finite or infinite) or union of finite intervals). Reality. .. A continuous random variable is used as a model for a quantity that, in principle, takes values in an interval (subset of the real line), even though every measurement scale is, in truth, discrete.
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section4.1-4.2-students_SP11 - Recap: Discrete...

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