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A firm's revenue, in $1000, is estimated by the equation R = 100 + 20A + X, where A, the advertisement expenditure in $1000s is known (non-random), and X - N(0, 900) for any value of A. a. Draw a sketch of the relationship E(R|A) and advertisement expenditure, where A varies from 0 to 5 (Note: This is a conditional expectation, E(R|A) = 100 + 20A) b. Compute the probability that the revenue is greater than $110,000 if advertisement expenditure is equal to $2000, P(R > 110|A = 2). Draw a sketch to illustrate c. Compute the probability that revenue is greater than $110,000 if advertising expenditure equals $3000, P(R > 110 | A = 3). your calculation.

A firm's revenue, in $1000, is estimated by the equation R = 100 + 20A + X, where A, the advertisement expenditure in $1000s is known (non-random), and X - N(0, 900) for any value of A. a. Draw a sketch of the relationship E(R|A) and advertisement expenditure, where A varies from 0 to 5 (Note: This is a conditional expectation, E(R|A) = 100 + 20A) b. Compute the probability that the revenue is greater than $110,000 if advertisement expenditure is equal to $2000, P(R > 110|A = 2). Draw a sketch to illustrate c. Compute the probability that revenue is greater than $110,000 if advertising expenditure equals $3000, P(R > 110 | A = 3). your calculation.

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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#3 a,b,c

3 A firm's revenue, in $1000, is estimated by the equation R = 100 + 20A + X, where A, the advertisement expenditure in $1000s is known (non-random), and X - N(0, 900) for any value of A. a. Draw a sketch of the relationship E(R|A) and advertisement expenditure, where A varies from 0 to 5 (Note: This is a conditional expectation, E(R|A) = 100 + 20A) b. Compute the probability that the revenue is greater than $110,000 if advertisement expenditure is equal to $2000, P(R > 110 A = 2). Draw a sketch to illustrate your calculation. c. Compute the probability that revenue is greater than $110,000 if advertising expenditure equals $3000, P(R > 110 | A = 3). d. Find the 25-th and the 95-th percentiles of the distribution of revenue when A = 2. [The p-th percentile is that value of R, R_p, such that P(R < R_p) = p]. e. Compute the level of advertisement expenditure to ensure that the probability of revenue being larger than $110,000 is 0.95. Show an explanatory graph.
Transcribed Image Text:3 A firm's revenue, in $1000, is estimated by the equation R = 100 + 20A + X, where A, the advertisement expenditure in $1000s is known (non-random), and X - N(0, 900) for any value of A. a. Draw a sketch of the relationship E(R|A) and advertisement expenditure, where A varies from 0 to 5 (Note: This is a conditional expectation, E(R|A) = 100 + 20A) b. Compute the probability that the revenue is greater than $110,000 if advertisement expenditure is equal to $2000, P(R > 110 A = 2). Draw a sketch to illustrate your calculation. c. Compute the probability that revenue is greater than $110,000 if advertising expenditure equals $3000, P(R > 110 | A = 3). d. Find the 25-th and the 95-th percentiles of the distribution of revenue when A = 2. [The p-th percentile is that value of R, R_p, such that P(R < R_p) = p]. e. Compute the level of advertisement expenditure to ensure that the probability of revenue being larger than $110,000 is 0.95. Show an explanatory graph.
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