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.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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