The distributor of a machine for cytogenics has developed a new model. The company estimates that when it is introduced into the market, it will be very successful with a probability 0.6, moderately successful with a probability 0.3, and not successful with probability 0.1. The estimated yearly profit associated with the model being very successful is $15 million and with it being moderately successful is $5 million; not successful would result in a loss of $500,000. Let X be the yearly profit of the new model. Determine the probability mass function of X.

Solution:

Step 1 of 2:

Given the problem states that, the probabilities for the company estimates that when it is introduced into the market, it will be very successful = 0.6, moderately successful = 0.3, or unsuccessful = 0.1.

The estimated yearly profit associated with the model being very successful is $15 million and moderately successful = $5 million, or unsuccessful would result in a loss of $500,000.