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#11




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I have to break up the range into 3 parts and then find the probability of each section and multiply by the conditional density. Therefore, the answer should look something like this. P(3<U<10/3X>10)*P(X>10) + P(10/3<U<5X>10)*P(X>10) + P(5<U<6X>10)*P(X>10) = Thank you again for your input and wish you happy holidays and a happy new year! 
#12




Quote:
The overall sum is in this form: Here is the sum in the same order: Then the integral within is an application of the continuous law of total probability. Here A is the event X>=10 given 10/3<U<5 and the pdf is of U(10/3<U<5)... it's just more complicated looking because we're within an outer use of the law of total probability. Happy Holidays and Happy New Year to you as well! Last edited by Z3ta; 12282017 at 08:11 PM.. 
#13




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Thank you. 
#14




Close to what I said. Even closer is that you need to think about the integrals for each of those three ranges (of the outer integral of the double integrals). Determining the upper and lower limits for each of those inside integrals will help you. Happy holidays and a happy new year to you, too, and good luck on the exam.

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