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#2




Are you asking for something like this? https://www.quora.com/Whatareexamp...sinreallife

#4




If you draw 2 random numbers between 0 and 1, the PDF of the larger of the two numbers is f(x) = 2x.
Fun Fact: This can actually be generalized more. If you draw n random numbers between 0 and 1, the PDF of the largest number is f(x) = n * x^(n  1). Expected value of the largest number is n / (n + 1).
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#8




With continuous random variables single points have zero probability. If f(x) = 2x, then F(x) = x^2, so the probability the larger of the two random numbers is less than .5 is .25. Let's say we want the probability that the larger of the two is between .4 and .6. We would integrate the pdf over that interval.

#9




Yes, the probability is 0.01. As pointed out by Academic Actuary later in the thread, probabilities are integrals of the density function, not the density function. The integral of the density function from 0 to .1 is .01.

#10




Quote:
The question is, how can we show that the pdf is actually f(x) = 2x in this case? 
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