052009 dr pierre elbischger mip1isapss09 12 continuous

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Unformatted text preview: d γ 1 −∞ Example: Uniform distribution 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 12 Continuous vs discrete random variable Discrete random variable A discrete random variable is one which may take on only a countable number of distinct values such as 0, 1, 2, 3, 4, ... Discrete random variables are usually (but not necessarily) counts. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, etc.. (e.g., Binomial distribution, Poisson distribution - count of the number of events that occur in a certain time interval or spatial area → CCD element ) Example: Binomial distribution n =) p ( X k= p k (1 − p ) n − k k Example: Bimodal distribution X has value 1 with probability p and -1 with probability (p-1). Mixed distribtuion Continuous random variable A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile. (e.g., Normal distribution). 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 13 Uniform / Impulse distribution Uniform 19.05.2009 Impulse Dr. Pierre Elbischger - MIP1/ISAP'SS09 14 Gaussian distribution (normal distribution) z N (µ ,σ 2 ) µ mean σ 2 variance P ( µ − σ < x ≤ µ − σ ) =7 0, P ( µ − 2σ < x ≤ µ − 2σ ) = 0,95 Mathematical tractable in both the spatial and frequency domain. Is appropriate in many realistic cases → central limit theorem. 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 15 Rayleigh distribution 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 16 Gamma / Exponential distribution Gamma 19.05.2009 Exponential Dr. Pierre Elbischger - MIP1/ISAP'SS09 17 E17 Histogramming Partition the measurement space into a finite number n of disjoint regions ℛi with equal volume Vn (1D width of the bins, 2D area, 3D volume, nD hypervolume) called bins, and count the number...
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This note was uploaded on 07/09/2009 for the course MEDIT 1 taught by Professor Pierreelschbinger during the Spring '09 term at Carinthia University of Applied Sciences.

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