2 $f(x)=\frac{2^{x}e^{-2}}{x}$\n3 $f(x)=\frac{2^{x}e^{2}}{x!}$\nequation #1\nb. what is the expected number…

2 $f(x)=\frac{2^{x}e^{-2}}{x}$\n3 $f(x)=\frac{2^{x}e^{2}}{x!}$\nequation #1\nb. what is the expected number of occurrences in three time periods?\n6\nc. select the appropriate poisson probability function to determine the probability of $x$ occurrences in three time periods.\n1 $f(x)=\frac{6^{x}e^{6}}{x!}$\n2 $f(x)=\frac{6^{x}e^{-6}}{x}$\n3 $f(x)=\frac{6^{x}e^{-6}}{x!}$\nequation #3\nd. compute the probability of two occurrences in one time period (to 4 decimals).\n0.2707\ne. compute the probability of six occurrences in two time periods (to 4 decimals).\n0.1055\nf. compute the probability of seven occurrences in three time periods (to 4 decimals).

2 $f(x)=\frac{2^{x}e^{-2}}{x}$\n3 $f(x)=\frac{2^{x}e^{2}}{x!}$\nequation #1\nb. what is the expected number of occurrences in three time periods?\n6\nc. select the appropriate poisson probability function to determine the probability of $x$ occurrences in three time periods.\n1 $f(x)=\frac{6^{x}e^{6}}{x!}$\n2 $f(x)=\frac{6^{x}e^{-6}}{x}$\n3 $f(x)=\frac{6^{x}e^{-6}}{x!}$\nequation #3\nd. compute the probability of two occurrences in one time period (to 4 decimals).\n0.2707\ne. compute the probability of six occurrences in two time periods (to 4 decimals).\n0.1055\nf. compute the probability of seven occurrences in three time periods (to 4 decimals).

Answer

Explanation:

Step1: Recall Poisson probability formula

The Poisson probability function is $f(x)=\frac{\lambda^{x}e^{-\lambda}}{x!}$, where $\lambda$ is the average number of occurrences in the given interval and $x$ is the actual number of occurrences.

Step2: For part f

We know from part b that for three - time periods $\lambda = 6$. We want to find the probability of $x = 7$ occurrences in three time periods. Substitute $\lambda=6$ and $x = 7$ into the Poisson formula: $f(7)=\frac{6^{7}e^{-6}}{7!}$ First, calculate $6^{7}=279936$, $e^{-6}\approx0.002479$, and $7!=5040$. Then $6^{7}e^{-6}=279936\times0.002479 = 693.961344$. $\frac{6^{7}e^{-6}}{7!}=\frac{693.961344}{5040}\approx0.1377$

Answer:

$0.1377$