Question

Please round answers to at least 6 decimal places, or type exact answers by using "e^(x)" to input e^x The Poisson distribution with parameter lambda = 0.591 has been assigned for the outcome of an experiment. Let XI be the outcome function. Find the probabilities, P(X = 0) =| P(X = 0) =| P(X = 0) =| P(X = 0) =| P(X 1) =| P(X > 1) =|

Answer 1

To find probabilities using the Poisson distribution with lambda = 0.591, formulas involving the exponential function and the respective power of lambda divided by factorial of the event number are used.

Step-by-step explanation:

The Poisson distribution with parameter lambda = 0.591 is used to find the probabilities of various outcomes for the random variable X, which represents the number of occurrences in a fixed interval. The probability of an event occurring zero times (X = 0) is calculated using the formula:

P(X = 0) = e^(-lambda) * lambda^0 / 0! = e^(-0.591) * 1 = e^(-0.591)

For finding P(X = 1), the formula becomes:

P(X = 1) = e^(-lambda) * lambda^1 / 1! = e^(-0.591) * 0.591

The probability of X being greater than 1 (P(X > 1)) is found by subtracting the probability of X being 0 or 1 from 1:

P(X > 1) = 1 - P(X = 0) - P(X = 1)