Every day a logistic service provider collects (used) oil at seventeen garages in the province of...

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Every day a logistic service provider collects (used) oil at seventeen garages in the province of Gelderland. She uses a small van with a 4-kiloliter tank inside. The total amount of oil (in kiloliters (1 kiloliter=1000 liter)) to be collected on a day is a continuous stochastic variable X with probability density function f(x): c if 2 sas 5 f(x) ={ (-cr + 7c)/2 if 5 <rs7 0 elsewhere Determine the value for c such that f(x) is indeed a probability density function. Show all your calculations. Every day a logistic service provider collects (used) oil at seventeen garages in the province of Gelderland. She uses a small van with a 4-kiloliter tank inside. The total amount of oil (in kiloliters (1 kiloliter=1000 liter)) to be collected on a day is a continuous stochastic variable X with probability density function f(x): c if 2 sas 5 f(x) ={ (-cr + 7c)/2 if 5 <rs7 0 elsewhere Determine the value for c such that f(x) is indeed a probability density function. Show all your calculations.