Hint: The joint CDF has X ≤ x X ≤ x and Y ≤ y Y ≤ y for 0 ≤ y ≤ x <∞ 0 ≤ y ≤ x <∞. Consider a fixed (x0,y0) (x 0, y 0) to eliminate confusion (each of these will actually be variable in the …

That sounds about right. Taking the derivative of the joint cdf with respect to e.g. y y just gives you the inner-most integral.

The CDF makes more sense in real-valued variables, but the definition of independence is described with PDF's, no? Also, does proving that the product of marginal PDF's equal the …

2018年5月10日 · If both the random variables were discrete (continuous) then we could have found the joint PMF (joint PDF). But since X X and Y Y are discrete and continuous, …

2021年3月24日 · Is this the definition of conditional probability of 2 continuous random variables conditioned on 1 continuous random variable? Please provide a reference. (I forgot if any 2 …

2019年9月1日 · Can someone explain how to find the joint CDF of this problem? Also can someone please explain to me how to evaluate the bounds to integrate cdf and how to create …

See these notes for more details, page 163. As for how to fix your approach: The second mixed derivative is negative for xy ≥ 1 x y ≥ 1. You're claiming that a probability density function can …

2018年7月29日 · Some other bounds are e.g. 0 <x <1 and 0 <y <x, but how do I find the CDF for this case? I can find some of the bounds, but don't know how to use them for the integrals.

You don't seem to have addressed the OP's actual question. They seem to be ok with calculating c c instead they seem to be asking about how to compute the joint cdf.

2018年9月1日 · I have f(x, y) = 3x f (x, y) = 3 x for 0 ≤ y ≤ x ≤ 1 0 ≤ y ≤ x ≤ 1 and I want to find F(x, y) F (x, y). In lecture, our prof showed us how to do this the following way: I tried replicating …