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A farmer has 100 kilograms of apples and 50 kilograms of potatoes for sale. The market price for apples (per kilogram) each day is a random variable with a mean of $0.50 and a standard deviation of $0.20. Similarly for a kilogram of potatoes the mean price is $0.30 per kilogram and the standard deviation is $0.10. The market is busy with eager shoppers, so it is reasonable to assume that the farmer will be able to sell all of each type of produce at that day's price.
a. Define your random variables and use them to express the farmer's daily revenue.
b. Find the mean daily revenue
c. Find the standard deviation of daily revenue assuming
1) That the daily prices for apples and potatoes are independent of each other
2) That the daily prices for apples and potatoes are positively correlated with a correlation coefficient of 0.4.
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