Question

At a four-way intersection, the number of traffic accidents during a month follows a Poisson distribution with a mean of 3. Define a random variable X as the number of accidents during a month, then X ~ Pois(3). (a) Find the probability of observing exactly two accidents at this intersection in one month. (b) What is the probability that less than 10 accidents occur in a quarter (a three-month period)? (c) Suppose you start monitoring one-month periods, one after another. Call them periods 1, 2, 3, ... etc. You record the number of traffic accidents per period. Assume time periods are independent of each other in terms of accidents etc. Define a success for each period as "time period had no traffic accident". Let Y = the time period in which the first success occurs. Give the distribution of Y and value(s) of any parameter(s). (Hint: What is the probability of no traffic accident in a one-month period?) (d) (2 points) Find P(Y > 3).

          At a four-way intersection, the number of traffic accidents during a month follows a Poisson distribution with a mean of 3. Define a random variable X as the number of accidents during a month, then X ~
Pois(3).

(a) Find the probability of observing exactly two accidents at this intersection in one month.

(b) What is the probability that less than 10 accidents occur in a quarter (a three-month period)?

(c) Suppose you start monitoring one-month periods, one after another. Call them periods 1, 2, 3, ... etc. You record the number of traffic accidents per period. Assume time periods are independent of each other in terms of accidents etc. Define a success for each period as "time period had no traffic accident". Let Y = the time period in which the first success occurs. Give the distribution of Y and value(s) of any parameter(s). (Hint: What is the probability of no traffic accident in a one-month period?)

(d) (2 points) Find P(Y > 3).

At a four-way intersection, the number of traffic accidents during a month follows a Poisson distribution with a mean of 3. Define a random variable X as the number of accidents during a month, then X
Pois(3).

(a) Find the probability of observing exactly two accidents at this intersection in one month.

(b) What is the probability that less than 10 accidents occur in a quarter (a three-month period)?

(c) Suppose you start monitoring one-month periods, one after another. Call them periods 1, 2, 3, ... etc. You record the number of traffic accidents per period. Assume time periods are independent of each other in terms of accidents etc. Define a success for each period as "time period had no traffic accident". Let Y = the time period in which the first success occurs. Give the distribution of Y and value(s) of any parameter(s). (Hint: What is the probability of no traffic accident in a one-month period?)

(d) (2 points) Find P(Y > 3).

Added by Josefina K.

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