P1. Lets say we have 2 random variables X~Uniformly(0,1) and Y~Uniformly(0,2)
Determine the probability P(X<Y).
I suspect the answer is 1/4, but I do now know how to formally get to this result.
P2. the same as above but this time X~Exp(1) and Y~Exp(2)
you need to review densities
and you need f(x,y) in both cases
in the first problem
f(y)=1/2 and f(x)=1 since these are uniforms
By indep the joint density is the product.
in the second question
and the density of Y can eithe be or
depending how you define the exponential distribution.