Discrete Mathematics

# Poisson Distribution

Passengers drop by a busy store at an average rate of $$\lambda = 4$$ per minute. If the number of passengers dropping by the store obeys a Poisson distribution, what is the approximate probability that $$16$$ passengers drop by the store in a particular $$4$$ minute period?

If a random variable $$X$$ obeys the Poisson distribution with mean $$2,$$ what is its variance $$\text{Var}(X)?$$

Assume that bacteria of a species called $$X$$ are randomly distributed in a certain river $$Y$$ according to the Poisson distribution with an average concentration of $$16$$ per $$40 \text{ ml}$$ of water. If we draw $$10 \text{ ml}$$ of water from the river using a test tube, what is the approximate probability that the number of bacteria $$X$$ in the sample is exactly $$4?$$

According to the maintenance department of a university, the number of toilet blockages obeys a Poisson distribution with an average of $$6$$ failures everyday. Then what is the approximate probability that there will be $$4$$ failures during a particular day?

Which of the following is the correct graph for the probability distribution of a random variable $$X$$ that follows the Poisson distribution with mean $$10?$$

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