Stats Solutions

(Step-by-Step) f(y 1 ,y 2)= 1, 0 ≤ y 1 ≤ 2, 0 ≤ y 2 ≤ 1, 2y 2 ≤ y 1 , 0, elsewhere Is a valid joint probability density function for Y 1 , the amount of pollutant

Question: f(y 1 ,y 2 )= 1, 0 ≤ y 1 ≤ 2, 0 ≤ y 2 ≤ 1, 2y 2 ≤ y 1 ,

0, elsewhere

Is a valid joint probability density function for Y 1 , the amount of pollutant per sample collected above the stack without the cleaning device, and Y 2 , the amount collected above the stack with the cleaner.

  1. Find E(Y 1 ) and E(Y 2 ).
  2. Find V(Y 1 ) and V(Y 2 ).
  3. The random variable Y 1 -Y 2 represents the amount by which the weight of pollutant can be reduced by using the cleaning device. Find E(Y 1 – Y 2 ).
  4. Find V(Y 1 –Y 2 ). Within what limits would you expect Y 1 –Y 2 to fall?

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


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