A bakery owner finds from his past experience that sale of number of chocolate cakes produced in his bakery on any day is a random variable X having the following probability distribution:
No. of cakes sold X=n
0
1
2
3
4
5
P(n)
1/6
1/6
1/6
1/6
1/6
1/6
He gets a profit of Rs.5 per each cake sold and incurs a loss of Rs.2 per cake not being sold. If the bakery owner produces 3 cakes on a given day what is the value of his expected profit?
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Answer:
expected profit = Rs 3
Step-by-step explanation:
Total cake = 3
on selling 0 cake profit = 0 & loss = 3 * 2 = 6
P(0) = 1/6
Loss = 6/6 = 1
on selling 1 cake profit = 5 & loss = 2 * 2 = 4
Net profit = 1
P(1) = 1/6
Profit = 1/6
on selling 2 cake profit = 2*5 = 10 & loss = 1 * 2 = 2
Net profit = 8
P(2) = 1/6
Profit = 8/6
on selling 3 cake profit = 3*5 = 15 & loss = 0 * 2 = 0
Net profit = 15
P(3) = 1/6
Profit = 15/6
Expected Profit = 15/6 + 8/6 + 1/6 - 1 = 3
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