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# Families of RV - FAMILIES OF RANDOM VARIABLES Poisson...

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FAMILIES OF RANDOM VARIABLES Poisson Arrival Process Arrivals occur ) ) Pr{ } ( ) Pr{ } 1 ( ) Pr{ } ( ) i memoryless ii One Arrival during t t o t No Arrival during t t o t Two or more Arrivals during t o t λ ∆= ∆+ ∆ ∆=− ∆+ ∆ ∆= We call as the arrival rate, and 1 as the mean inter-arrival time. time t n t n+1 t n-1 t 0 t 1 . . . C n C n+1 C n-1 C 0 C 1

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We can show 1) Pr{ k arrivals during time [0, t ]} is Poisson () ! k t k t Pt e k λ = 2) Inter-arrival time = 1 nn tt is exponential , 0 x X fx e x =
Central Limit Theorem Let 12 , ,, n XX X be a sequence of i.i.d. random variables each with mean µ and variance 2 σ . Define . Then lim (0,1). n n

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Families of RV - FAMILIES OF RANDOM VARIABLES Poisson...

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