Each rear tire on an experimental airplane is supposed to be filled to a pressure of 40 pounds per square inch (psi). Let Y₁ denote the actual air pressure for the right tire and Y₂ denote the actual air pressure for the left tire. Suppose that Y₁ and Y₂ are random variables with the joint density function k (y² + y2), 30 ≤ Y1, Y2 < 50 elsewhere f (y₁, y2) = a) Find k. b) Find the joint distribution function for Y₁ and Y₂. c) Find the probability that both tires are underfilled.

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