The purpose of solving Poisson distribution homework is to analyze and calculate the probability of a specific number of events occurring within a given time or space interval. This is useful in various fields such as economics, biology, and engineering, where random occurrences need to be predicted and managed.
To find f(y) in Poisson distribution, you need to use the formula f(y) = (e^-λ * λ^y)/y!, where λ is the average number of events occurring in the given interval and y is the number of events you want to calculate the probability for.
The main difference between Poisson distribution and normal distribution is that Poisson distribution is used to calculate the probability of a specific number of events occurring in a given interval, while normal distribution is used to calculate the probability of a continuous variable falling within a certain range.
The assumptions of Poisson distribution include a constant rate of occurrence of events, events occurring independently of each other, and a fixed time or space interval in which the events are observed.
There are a few ways to check if your data fits a Poisson distribution. You can plot a histogram of your data and see if it follows a bell-shaped curve, which is characteristic of Poisson distribution. You can also use statistical tests such as the chi-square goodness of fit test to determine the fit of your data to the Poisson distribution. Additionally, you can compare your data to the expected values calculated using the Poisson distribution formula.