Independent Poisson variates refer to two random variables that follow a Poisson distribution and are not affected by each other's outcomes. This means that the occurrence of one variable does not affect the probability of the other variable occurring.
You can determine if two variables are independent Poisson variates by calculating their correlation coefficient. If the correlation coefficient is close to 0, then the variables are likely independent. Additionally, you can plot the variables on a scatterplot to visually examine any patterns or relationships.
The formula for the Poisson distribution is P(x) = (e^-λ * λ^x) / x!, where λ is the mean or expected value of the distribution and x is the number of occurrences.
Yes, two variables can have different values for λ and still be independent Poisson variates. The independence of the variables is determined by their correlation coefficient, not their mean values.
Some real-life examples of independent Poisson variates include the number of customers visiting a store in a given time period and the number of accidents occurring on a highway segment in a given day. In both cases, the occurrences of one variable do not affect the probability of the other variable occurring.