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) option (ii) (b) compute f(2). (c) compute f(1). (d) compute p(x ≥ 2).

Answer 1

The appropriate Poisson probability mass function for a Poisson distribution with μ = 4 is option (ii). To compute f(2), substitute x = 2 into the PMF. To compute P(x ≥ 2), use the CDF and subtract the probability of x < 2 from 1.

Step-by-step explanation:

The appropriate Poisson probability mass function for a Poisson distribution with μ = 4 is option (ii). This means that the probability mass function (PMF) is given by f(x) = e^(-4) * (4^x) / x!.

To compute f(2), we substitute x = 2 into the PMF formula: f(2) = e^(-4) * (4^2) / 2! = 0.1465 (rounded to four decimal digits).

To compute f(1), we substitute x = 1 into the PMF formula: f(1) = e^(-4) * (4^1) / 1! = 0.1465 (rounded to four decimal digits).

To compute P(x ≥ 2), we can use the cumulative distribution function (CDF): P(x ≥ 2) = 1 - P(x < 2) = 1 - P(x ≤ 1) = 1 - f(0) - f(1) = 1 - e^(-4) - e^(-4) * (4^1) / 1! = 0.8647 (rounded to four decimal digits).