1. Calculate the probabilities based on the given data. The probability of observing Xi (Example: based on the provided data, the probability of receiving 3 jobs at the job shop is 14/1023). Label the column of probabilities Yi.

2. Using the formula of Poisson distribution given above, calculate (i) for each i (hint: initially take = 9). Do not use the built-in Poisson function of Excel.

3. For each ", compute (") "

4. For each ", compute ((") ")C

5. Compute "((") ")C

6. Use the Solver to minimize the error ("((") ")C), by changing the value of .

In the attached Excel file, you are given the data about the number of jobs arrived at a job shop over a period of 1023 days. Column Xi gives the possible number of jobs arrived in a day and column "Occurrences provides the number of days (among 1023) in which x jobs arrived at the job shop. The goal is to fit a Poisson distribution to this data. The Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space. The Poisson distribution can be written as p(x) = ea - x 10, x=0,1,... otherwise Poisson distribution has only one parameter, which represents both E(X) and V(X) of the distribution. Example: The number of customers arriving at a bakery follows a Poisson distribution with mean 10. What is the probability of observing five customers in a day? Answer: Mean-10 -10 P(5) = 10109 = 3.8% Fit a Poisson distribution to the data given in the Excel file following the steps below: 1. Calculate the probabilities based on the given data. The probability of observing xis Occurences (X) Occurences (X) (Example: based on the provided data, the probability of receiving 3 jobs at the job shop is 14/1023). Label the column of probabilities y 2. Using the formula of Poisson distribution given above, calculate f(x) for each x (hint: initially take a 9). Do not use the built-in Poisson function of Excel. 3. For each Xi, compute f(x) y 4. For each X, compute (f(x)- y.) 5. Compute :(x)- y.) 6. Use the "Solver" to minimize the error (Of(x)- y.)), by changing the value of a Submit your Excel file with the optimized value of a Homework alpha RSS Occurrences yi fi) fi)-yi (fi)-vilu2 SUM((fi)-viy^2) WN WO 35 36 Poisson Distribution + In the attached Excel file, you are given the data about the number of jobs arrived at a job shop over a period of 1023 days. Column Xi gives the possible number of jobs arrived in a day and column "Occurrences provides the number of days (among 1023) in which x jobs arrived at the job shop. The goal is to fit a Poisson distribution to this data. The Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space. The Poisson distribution can be written as p(x) = ea - x 10, x=0,1,... otherwise Poisson distribution has only one parameter, which represents both E(X) and V(X) of the distribution. Example: The number of customers arriving at a bakery follows a Poisson distribution with mean 10. What is the probability of observing five customers in a day? Answer: Mean-10 -10 P(5) = 10109 = 3.8% Fit a Poisson distribution to the data given in the Excel file following the steps below: 1. Calculate the probabilities based on the given data. The probability of observing xis Occurences (X) Occurences (X) (Example: based on the provided data, the probability of receiving 3 jobs at the job shop is 14/1023). Label the column of probabilities y 2. Using the formula of Poisson distribution given above, calculate f(x) for each x (hint: initially take a 9). Do not use the built-in Poisson function of Excel. 3. For each Xi, compute f(x) y 4. For each X, compute (f(x)- y.) 5. Compute :(x)- y.) 6. Use the "Solver" to minimize the error (Of(x)- y.)), by changing the value of a Submit your Excel file with the optimized value of a Homework alpha RSS Occurrences yi fi) fi)-yi (fi)-vilu2 SUM((fi)-viy^2) WN WO 35 36 Poisson Distribution +