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I come with a question I was hoping soemone out there can help me set up.

"The manager of a bakery knows that the number of chocalate cakes he can sell on any given day is a random variable with the probability mass function:

p(x)=1/6 For x=0,1,2,3,4,5

Also, there is a profit of 1$ on each cake sold and a loss of .40$ on each cake he doesn't sell (on a given day). Assuming each cake can only be sold on the day it was made, Find the baker's profit for a day when he bakes 5 chocalate cakes"

The hint is: Let the random vairable Y be the actual daily profit or loss. Using the probability distribution for X (number of customers asking for cakes) find the probability distribution for Y. The probability distribution for Y will depend on the number of cakes you decide to bake that day. You can answer the question using the random variable Y. Be careful to consider the possibility that the demand for your cakes, X, may exceed your supply.

With that said, my problem is this. I don't quite understand the problem and can't set it up. I have tried using the binomial distribtution. But don't understand how to actually get the profit.

Any help with this would be greatly appreciated.

Thanks,

Disar