Probability

Discrete Probability Distributions

Poisson Distribution

         

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

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

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

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

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

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