The expected number of car accidents in an intercity highway in a month is known as 4.5, (i.e. it has is known to be = 4.5). The number of accidents is known and to have a Poisson distribution. a) Compute the probability of exactly no accident in a month b) Compute the probability of exactly 1 accident in a month c) Compute the probability of at most 2 accidents in a month d) Compute the probability of at least 4 accidents in a month. e) Compute the probability of at most 4 accidents in a month, if it is known that there were at least 2 accidents. (Assume that the number of accidents for a month in the city follows a Poisson distribution)

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The expected number of car accidents in an intercity highway in a month is known as 4.5, (i.e. it has is known to be = 4.5). The number of accidents is known and to have a Poisson distribution.
a) Compute the probability of exactly no accident in a month
b) Compute the probability of exactly 1 accident in a month
c) Compute the probability of at most 2 accidents in a month
d) Compute the probability of at least 4 accidents in a month.
e) Compute the probability of at most 4 accidents in a month, if it is known that there were at least 2 accidents. (Assume that the number of accidents for a month in the city follows a Poisson distribution)

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