(Solved): Consider a Poisson distribution with a mean of two occurrences per time period. a. Which of the fol ...

Consider a Poisson distribution with a mean of two occurrences per time period. a. Which of the following is the appropriate Poisson probability function for one time period? \( 1 f(x)=\frac{2^{x} e^{-2}}{x !} \) \( 2 f(x)=\frac{2^{x} e^{-2}}{x} \) \( 3 f(x)=\frac{2^{x} e^{2}}{x !} \) b. What is the expected number of occurrences in three time periods? c. Select the appropriate Poisson probability function to determine the probability of \( x \) occurrences in three time periods. \( 1 f(x)=\frac{6^{x} e^{6}}{x !} \) \( 2 f(x)=\frac{6^{x} e^{-6}}{x} \) \( 3 f(x)=\frac{6^{x} e^{-6}}{x !} \) \( 1 f(x)=\frac{}{x !} \) \( 2 f(x)=\frac{6^{x} e^{-6}}{x} \) \( 3 f(x)=\frac{6^{x} e^{-6}}{x !} \) d. Compute the probability of three occurrences in three time periods (to 4 decimals). e. Compute the probability of six occurrences in two time periods (to 4 decimals). f. Compute the probability of five occurrences in one time period (to 4 decimals).