Solving a probability distribution problem in profit contract

A contractor has submitted bid on four state jobs: a car parking garage, an office building, a theater, and a shopping mall. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are: RM2 million from the parking garage, RM3 million from the office building, RM5 million from the theater, and RM7 million from the shopping mall. He gets no profit if he does not get any contract.

The contractor estimates that the probabilities of getting the car parking garage contract, the office building contract, the theater contract, the shopping mall contract, or nothing are 0.25, 0.15, 0.35, 0.13, and 0.12 respectively.

Let Y be the random variable that represents the contractor’s profits in millions of ringgits.

1. Write the probability distribution of Y. (4 marks)

2. Construct the cumulative probability distribution of Y (4 marks)

3. Find the expected profit of the contractor. Give a brief interpretation of the value obtained (5 marks)

4. Estimate the probability of the profit more than what is expected by the contractor. (2 marks)

• see the faq on how this site works. Homework questions are answered here, but more effort must be put in by the person asking. – mpiktas May 6 '12 at 8:00
• to start with, try to rephrase in your question the problem without the "story" on top of it, namely Y takes such and such values, with probability this much and that much, which is essentially question 1. – Xi'an May 6 '12 at 8:08
• I like the problem posed the way it is. It makes it more interesting. – Michael R. Chernick May 6 '12 at 15:34
• I think Xi'an didn't mean it as a criticism, he gave a hint that rephrasing it without the story basically already gives you the answer to 1. – Erik May 6 '12 at 16:01