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Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) 2y 0≤ y ≤1 0 otherwise The industry is paid 500 dollars daily per ton of metal mixture whereas there is also a fixed transportation cost of 200 dollars per day. Let W be the industry's daily income (in hundreds of dollars). a) Find the probability density function of W. b) What is the industry's expected and median daily income? (round to 2 decimal places)

Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) 2y 0≤ y ≤1 0 otherwise The industry is paid 500 dollars daily per ton of metal mixture whereas there is also a fixed transportation cost of 200 dollars per day. Let W be the industry's daily income (in hundreds of dollars). a) Find the probability density function of W. b) What is the industry's expected and median daily income? (round to 2 decimal places)

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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Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) = √2y 0<y≤1 0 otherwise The industry is paid 500 dollars daily per ton of metal mixture whereas there is also a fixed transportation cost of 200 dollars per day. Let W be the industry's daily income (in hundreds of dollars). a) Find the probability density function of W. b) What is the industry's expected and median daily income? (round to 2 decimal places)
Transcribed Image Text:Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) = √2y 0<y≤1 0 otherwise The industry is paid 500 dollars daily per ton of metal mixture whereas there is also a fixed transportation cost of 200 dollars per day. Let W be the industry's daily income (in hundreds of dollars). a) Find the probability density function of W. b) What is the industry's expected and median daily income? (round to 2 decimal places)
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