Question

# A company is about to develop and then market a new product. It wants to build...

A company is about to develop and then market a new product. It wants to build a simulation model for the entire process, and one key uncertain input is the development time, which is measured in an integer number of months. Company experts believe the development time will fall into the range of 5 to 9 months.They believe the probabilities of the extremes are both 10%, and the probabilities will vary linearly from those endpoints to a most likely value at 7 months. Choose an “appropriate” distribution, identify/state its parameters, and explain your choice.

Let X:the development time in months

The appropriate probability distribution is as follows

 X 5 6 7 8 9 P(X=x) 0.1 0.2 0.3 0.2 0.1

This is a discrete probability distribution and the parameters are X that is number of months for development and P(X=x) is the probability assigned to it.

Why this choice of model ?

i) The maximum probability occurs at 7 which is given in the question and hence that constraint is satisfied.

ii) One more constraint is the probability should vary linearly and hence in the above model it does happen.

iii) The probabilitiies sum up to 1 which indicates this is a correct probability distribution.

Thank you !!

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