Discrete Probability Distributions
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?
