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2. A retailer for a petroleum product sells a random amount X each day. Suppose that X, measured in thousands of gallons, has the probability density function f(x) {* 3x² 0≤x≤2 otherwise 1 The retailer's profit turns out to be $100 for each 1000 gallons sold (10 cents per gallon) if X ≤ 1 and $40 extra per 1000 gallons (an extra 4 of cents per gallon) if X > 1. Find the retailer's expected profit for any given day.

2. A retailer for a petroleum product sells a random amount X each day. Suppose that X, measured in thousands of gallons, has the probability density function f(x) {* 3x² 0≤x≤2 otherwise 1 The retailer's profit turns out to be $100 for each 1000 gallons sold (10 cents per gallon) if X ≤ 1 and $40 extra per 1000 gallons (an extra 4 of cents per gallon) if X > 1. Find the retailer's expected profit for any given day.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 1E
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2. A retailer for a petroleum product sells a random amount X each day. Suppose that X, measured in thousands of gallons, has the probability density function f(x) √³x² 0≤x≤2 {* {200 otherwise = 1 The retailer's profit turns out to be $100 for each 1000 gallons sold (10 cents per gallon) if X ≤ 1 and $40 extra per 1000 gallons (an extra 4 of cents per gallon) if X > 1. Find the retailer's expected profit for any given day.
Transcribed Image Text:2. A retailer for a petroleum product sells a random amount X each day. Suppose that X, measured in thousands of gallons, has the probability density function f(x) √³x² 0≤x≤2 {* {200 otherwise = 1 The retailer's profit turns out to be $100 for each 1000 gallons sold (10 cents per gallon) if X ≤ 1 and $40 extra per 1000 gallons (an extra 4 of cents per gallon) if X > 1. Find the retailer's expected profit for any given day.
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