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Discrete Probability Distributions

What is the probability that the sum of two dice will be less than 5? How many throws will it take you to hit your first "bullseye" on a dart board? Use discrete probability distributions to find out!

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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