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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

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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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