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Problema 3 Una persona se prepara para cruzar la calle a mitad de cuadra (es decir, no necesariamente en una intersection semaforizada o un paso

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Problema 3 Una persona se prepara para cruzar la calle a mitad de cuadra (es decir, no necesariamente en una intersection semaforizada o un paso de cebra). Para cruzar la calle requiere de "s" segundos. El trafico en la calle sigue un proceso de poisson de tasa ^ (autos por segundo). a.- Suponga que la persona no mira al cruzar. Calcule la probabilidad de que pueda cruzar sin ser atropellada por un auto. b.- Suponga ahora que la persona cruzara la calle luego de que pase el tercer auto. { Cuanto es el tiempo que demorara en cruzar la calle? Considere que actualmente se encuentro en el tiempo t = 0. c.=/Cual es la probabilidad que el tiempo transcurrido entre dos autos consecutives sea inferior a r minutos?. d.- La probabilidad que entre dos llegadas sucesivas sea superior a 10 segundos. Problema 5 Considere {N(t), t > 0} un Proceso Poisson que cuenta la cantidad de personas que llegan a un Banco. La tasa de llegadas es ^ personas por hora. Calcule: a.- La probabilidad de que no lleguen personas en un minuto dado. b.- La probabilidad que entre las 2 y las 4 lleguen 5 personas si es que entre las 1 y las 3 llegaron 2 personas. c.- La probabilidad de que entre dos llegadas consecutives pasen exactamente h minutos. d.- La probabilidad de que entre dos llegadas consecutives pasen al menos g segundos.m3 A person prepares to cross the street midblock (1g, albeit at a signalized intersection or zebra crossing). To cross the street requires "s" seconds. Traffic on the street follows a Poisson process at rate it (cars per second). a. Suppose the person does not look when crossing. Find the probability that she can cross without being hit by a car. b. Suppose now that the person will cross the street after the third car passes. How long will it take to cross the street? Consider that you are currently in time i=0. c.What is the probability that the time elapsed between two consecutive cars is less than 1\" minutes? d. The probability that between two successive arrivals is mm 10 gm. problem 5 Consider {N{t), t 23- U} a Poisson Process that counts the number ofpeople arriving at a Bank. The arrival rate is 1. persons per hour. Calculate: a. The probability that no people will arrive in a given minute. b. The probability that between 2 and 4 o'clock 5 people arrive if between 1 and 3 o'clock they arrived 2 people. c. The W thatexactly 11 minutes pass between two consecutive arrivals. d. The probability that at least g seconds pass between two consecutive arrivals

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