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Do The Math

Let T1 be the time between a car accident and reporting a claim to the insurance company. Let T2 be the time between the report of the claim and payment of the claim. The joint density function of T1 and T2, f(t1, t2), is constant over the region 0 < t1 < 6, 0< t2 < 6, t1 + t2 < 10, and zero otherwise. Determine E[T1 + T2], the expected time between a car accident and payment of the claim.

  1. 4.9
  2. 5.0
  3. 5.7
  4. 6.0
  5. 6.7

Solution: C
Let denote the joint density function of. The domain of f is pictured below:


 

 

 

 

 

 

 

Now the area of this domain is given by

 

 

Consequently,

 

 

and