Question

In a Poisson distribution, μ=0.4. (Round your answers to 4 decimal places.) a. What is the probability that x=0 ? b. What is the probability that x>0 ? Compute the mean and vartance of the following discrete probability distribution, (Round your answers to 2 decimal places.) Click hece tor the Excel Data File

Answer 1

To calculate the probability that x=0 for a Poisson distribution with mean μ=0.4, we use the probability mass function and find it to be approximately 0.6703. To find the probability that x>0, we subtract this value from 1 to get 0.3297. The distribution has a mean of 0.4, with variance also being 0.4 and the standard deviation approximately 0.63.

Step-by-step explanation:

The Poisson distribution is used to model the probability of a number of events occurring within a fixed interval of time or space. For a Poisson distribution with a mean (μ) of 0.4:

1. To find the probability that x=0, which is P(X=0), we use the Poisson probability mass function: P(X=x) = (μx * e−μ) / x!. Substituting in the values for x=0 and μ=0.4, we get P(X=0) = (0.40 * e−.4) / 0! = 0.6703 after rounding to four decimal places.
2. To find the probability that x>0, we subtract the probability that x=0 from 1: P(X>0) = 1 - P(X=0). Using the previously calculated P(X=0), we get P(X>0) = 1 - 0.6703 = 0.3297 after rounding to four decimal places.
3. The mean of the Poisson distribution is given by μ, which in this case is 0.40.
4. The variance of the Poisson distribution is also μ, so the variance is also 0.40.
5. The standard deviation is the square root of the variance, giving us a standard deviation of √0.40, which is approximately 0.63 when rounded to two decimal places.