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## Homework Statement

A gas supply company is trying to set up contracts with two clients, A and B. The company will make a profit of ten million dollars for each contract that is successfully agreed. The probability of agreeing a deal with client A is 1/4 and the probability of agreeing a deal with client B is 1/2. The decisions of the two clients are independent. Let X be the total profit that the company will make from the two clients.

a)Find the probability mass function of X

b)Find the mean and variance of X

## The Attempt at a Solution

I'm having a problem with setting up the PMF for this question.

f_X(x) =

1/4 for X = A

1/2 for X = B

This makes absolutely no sense. Furthermore, the sum of PMF has to equal to 1 but in this case, it isn't. I'm completely lost, how do I set up the PMF for this?

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