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Seeking solution for a problem about uniform distribution function.

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  • Seeking solution for a problem about uniform distribution function.

    An insurer estimates that Smith's time until death is uniformly distributed on the interval[0,5] and Jone's time until death is uniform on the interval[0,10]. the insurer assumes that the two times of death are independent of one another. Find the probability that Smith is the first of the twoto die.








    A 1/4 B.1/3 C 1/2 D2/3 E3/4

  • #2
    So you want P(Smith dies first) * P(Jone lives to the moment until Smith dies and Jone dies right after). Integrate that over appropriate region.

    P.S. this is very similar to MLC problems you will encounter in multiple lives section.

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    • #3
      I got 1/2. Is that correct?

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      • #4
        Incidentally you can also solve this problem without integration and just use the areas of the PDF since it is a uniform distribution. But you're answer of 1/2 is incorrect.

        Give it another shot!

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        • #5
          Hmm, so should it be 25/100 then?

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          • #6
            The area of the sample space is 5*10=50, so the joint pdf is 1/50. The probability that Jones lives longer is what the question is asking us to calculate. This means we want the area of the graph similar to Y>X where Y is Jones and X is Smith. This is not a square so take 1 - area of X>Y. That is 1 - (5*5*0.5)/50 = 1 - 12.5/50 or 1 - 25/100 = 0.75 or 3/4. Answer E is correct.
            Dan Kamka
            P/1, FM/2

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