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A manufacturer subscribes to an insurance policy for his factory. Let X be the value of...

A manufacturer subscribes to an insurance policy for his factory. Let X be the value of damage incurred by machinery in the factory and Y be the value of damage incurred by other components of the factory (e.g., building, furniture, etc.). The joint probability density function of the random variables X and Y is given by

f ( x , y ) = K y , x ≥ 0 , y ≥ 0 , x + y ≤ 1 for some constant K , and it is zero otherwise.

(a) Find the value of the normalizing constant K .

(b) Derive the marginal probability density functions of X and Y .

(c) Find the probability that the claim for damage to machinery ( X ) is smaller than the claim for the rest of the property ( Y ).

Math   Statistics-And-Probability   
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