Suppose that, on average, the number of car accidents in Hong Kong are
lilyta79jd
Answered question
2021-11-27
i. Determine the probability that at least χ accidents will occur in 12 hour period.
ii. In a two days, if there were 8 car accidents in Hong Kong, what is the probability that 2 accidents have occurred in the first 12 hours of the two days?
Answer & Explanation
breisgaoyz
Beginner2021-11-28Added 14 answers
Step 1
There are two different types of probability distributions: discrete and continuous. Poisson distribution is a discrete probability distribution.
Poisson distribution is deals with the probability of occurring a number of events in a period of time. There are only one parameter for Poisson distribution, that is . The mean and variance of the Poisson distribution is same as .
Step 2
Let X represent the total number of auto accidents in the 24-hour period in location H. It is assumed that six accidents occur every day. Therefore, X follows a Poisson distribution with parameter .
i) If for 24 hours, for 12 hours will be . Therefore, Y denotes a Poisson random variable with . The probability mass function of the Poisson distribution is given below.
indicates the probability that at least x accidents occur in the 12 hour period and it be calculated and it can be calculated in the following way.
So is the required probability.
Step 3
ii) Let X indicates the number of car accidents in place H in 24 hours period. it is given that 6 accidents occurs in 24 hour period. Thus X follows a Poisson distribution with parameter . Thus for 48 hours the will be 12.
P, the Poisson random variable for the number of accidents in the first 12 hours of a day, a week, or a month, shall be denoted. So . That is . Q denotes the number of accidents in the rest 36 hours of 48 hour period. Thus , thus
Given that 8 car accidents are taken place and the probability for happening 2 accidents in the first 12 hour period has to be calculated (2 happened in the first 12 hours and 6 happened in the rest 36 hours).
Therefore,
Hence, 0.31147 is the required probability.
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