A consultant has presented his client with three alternative research studies that could be conducted. If the client chooses alternative a, the consultant will have to hire 1 additional employee. Two new employees will have to be hired if the client chooses b, and 5 if the client chooses c.
The probability that the client will select alternative a is 0.1, with P(c) = 0.5 and P(c) = 0.4. Identify the discrete random variable in this situation and determine its expected value.