# Estimate / justification

It is difficult to make budgetary projections in the current economic climate. In particular, a decision regarding long-range planning will be made, in part, using the likelihood that the current recession will last less than 1.5 years. To estimate this probability, information from all previous recessions in the United States has been gathered. Of the 18 previous recessions, exactly 6 lasted less than 1.5 years. Assuming that the current recession is an observation from the same random experiment that produced the previous recessions (while admitting that this assumption is probably not strictly true) please produce a reasonable estimate of the probability that the current recession will last less than 1.5 years and justify the estimate.

Estimate:

Justification:

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It is difficult to make budgetary projections in the current economic climate. In particular, a decision regarding long-range planning will be made, in part, using the likelihood that the current recession will last less than 1.5 years. To estimate this probability, information from all previous recessions in the United States has been gathered. Of the 18 previous recessions, exactly 6 lasted less than 1.5 years. Assuming that the current recession is an observation from the same random experiment that produced the previous recessions (while admitting that this assumption is probably not strictly true) please produce a reasonable estimate of the probability that the current recession will last less than 1.5 years and justify the estimate.

Estimate:

The previous data shows that there are recessions lasting less than 1.5 years out of the sample of recessions. The estimate of the probability of the current recession lasting less than 1.5 years is:

Justification:

In this case we assume that X, the number of recessions out of the last 18, follows a binomial probability distribution with parameters . This means we assume that our sample of recessions are a set of 18 independent trials from the set of all recessions, each having the same probability of lasting less than less than 1.5 years. Using the binomial probability model, the best estimate of , the probability that a randomly selected recession lasts less than 1.5 years is:

Â© BrainMass Inc. brainmass.com December 24, 2021, 8:06 pm ad1c9bdddf>https://brainmass.com/statistics/probability/estimate-justification-247332