Quote:
Originally Posted by dslee85
So if I'm understanding this correctly this is what you are saying.
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!

You've got it a little mixed up dslee85.
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!