Exercises. 1. Using the Poisson formula, find the following probabilities

1. Using the Poisson formula, find the following probabilities

a) for

b) for

2. Let x be a Poisson random variable. Using the Poisson probabilities table, write the probability distribution of x for each of the following. Find the mean and standard deviation for each of these probability distributions.

a) ; b)

3. An average of 7.5 crimes are reported per day to police in a city. Use the Poisson formula to find the probability that

a) exactly 3 crimes will be reported to a police on a certain day

b) at least 2 crimes will be reported to a police on a certain day.

4. A mail-order company receives an average 1.3 complaints per day. Find the probability that it will receive

a) exactly 3 complaints

b) 2 to 3 complaints

c) more than 3 complaints

d) less than 3 complaints on a certain day.

5. An average of 4.5 customers come to the bank per half hour.

a) Find the probability that exactly 2 customers will come to this bank during a given hour;

b) Find the probability that during a given hour, the number of customers who will come to the bank is at most 2.

6. An average of 0.6 accidents occur per month at a large company.

a) Find the probability that no accident will occur at this company during a given month.

b) Find the mean, variance, and standard deviation of the number of accidents that will occur at this company during a given month.

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