Question

Consider a poisson distribution with μ = 4. if needed, round your answer to four decimal digits. (a) choose the appropriate poisson probability mass function. (i) (ii) (iii) (iv)

Answer 1

The student's question pertains to the Poisson distribution with a mean of 4, where probabilities for specific numbers of events are calculated using the Poisson probability mass function, and answers are rounded to four decimal places.

Step-by-step explanation:

The student has asked about calculating specific probabilities using the Poisson distribution with a mean (μ) of 4. In mathematical notation, this is represented as X~Poisson(4), meaning the random variable X follows a Poisson distribution with a mean of 4. The appropriate probability mass function (pmf) for a Poisson distribution is given by P(X = x) = (e-μ * μx) / x!, where x is the number of events (in this case, calls per minute), μ is the mean number of events, and e is Euler's number (approximately 2.71828).

For example, if we want to find P(X = 5), we substitute μ = 4 and x = 5 into the pmf to get P(X = 5) = (e-4 * 45) / 5! = (0.0183 * 1024) / 120 ≈ 0.1563, rounding to four decimal places. Other probabilities such as P(X ≤ 4) or P(X ≥ 8) can be found using similar calculations or technology such as a calculator with Poisson distribution functions.