TAILIEUCHUNG - LECTURE 7: CONTINUOUS DISTRIBUTIONS AND POISSON PROCESS

Consider a roulette wheel which has circumference 1. We spin the wheel, and when it stops, the outcome is the clockwise distance X from the “0” mark to the arrow. | Probability in Computing LECTURE 7 CONTINUOUS DISTRIBUTIONS AND POISSON PROCESS 2010 Quoc Le Van Nguyen Probability for Computing 1 Agenda Continuous random variables. Uniform distribution Exponential distribution Poisson process Queuing theory 2010 Quoc Le Van Nguyen Probability for Computing 2 Continuous Random Variables Consider a roulette wheel which has circumference 1. We spin the wheel and when it stops the outcome is the clockwise distance X from the 0 mark to the arrow. Sample space Q consists of all real numbers in 0 1 . Assume that any point on the circumference is equally likely to face the arrow when the wheel stops. What s the probability of a given outcome x Note In an infinite sample space there maybe possible events that have probability 0. Recall that the distribution function F x Pr X x . and f x F x then f x is called the density function of F x . 2010 Quoc Le Van Nguyen Probability for Computing

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