The monthly profit of a firm is given by the difference between total revenue and total cost for a given month: T = R – C where r is monthly profit in billions of dollars and R and C are, respectively, the corresponding

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1. Linear Combination of Random Variables
The monthly profit of a firm is given by the difference between total revenue and total cost
for a given month:
T = R – C
where r is monthly profit in billions of dollars and R and C are, respectively, the corresponding
revenue and costs of the firm in billions of dollars. Due to unpredictability of product price
and cost of production, R and C are both random variables with the following distribution:
N(86, 25)
C ~ N(31, 16)
and the covariance between total revenue and cost is 10
a. What is the expected value of profit for next month?
b. What is the standard deviation of the profit for the next month?
c. What is the probability that next month's profit is less than 47.46 billion of dollars?
Transcribed Image Text:1. Linear Combination of Random Variables The monthly profit of a firm is given by the difference between total revenue and total cost for a given month: T = R – C where r is monthly profit in billions of dollars and R and C are, respectively, the corresponding revenue and costs of the firm in billions of dollars. Due to unpredictability of product price and cost of production, R and C are both random variables with the following distribution: N(86, 25) C ~ N(31, 16) and the covariance between total revenue and cost is 10 a. What is the expected value of profit for next month? b. What is the standard deviation of the profit for the next month? c. What is the probability that next month's profit is less than 47.46 billion of dollars?
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