Recent content by rudders93

Thanks!

I think I've understood this now! Thanks so much BrownianMan! Changing the order of integration, we'd get: \int_0^1 \int_0^y \lambda x y^{2} dx dy = 1 and the way I determined that was graphically by seeing the area over which we're cycling over. So the inner integral, we're holding y constant...

I'll will look over that. Thanks!

Hmmm. I still don't understand this I think So is this what is happening? The first integral, \int_x^1 \lambda x y^{2} dy finds the area by subtracting the integral of y=1 from that of y=x. in the region that 0<=y<=1. Then you somehow integrate this region over 0<x<1? Atleast I think...

Oh, that definitely clears things up! So using that we've restricted the region of the graph. Now if I was to graph the x,y plane, the relationship between x and y would be y = +- x^2. But as we have a restricted region, and the line y=x , y=0, x=1, x=0 bound that region, which is contained...

Hi, thanks for response! Could you explain how you arrived at 0<=x<=y<=1 being the triangular region between the y axis, the line x=1, y=x, and y=1?

Hi, Thanks for reply. Yep my bad. But why does that integral work? How did they decide to do that?

Homework Statement Find λ given that the joint PDF of random variables X, Y, is given by: f(x,y)=\lambda x y^{2} where 0\leq x\leq y\leq 1 and 0 otherwise I have two questions: 1) How do I graph this? I'm not sure how to approach the inequality and graphing. What does this inequality...

Homework Statement Consider the following intervals: A = [-3,5), B = (3,8), C = (0,4] Find: A\capB and A\capC The Attempt at a Solution I thought that: A\capB=(3,5) and that A\capC=[0,4] as that is the intersection point, but this book (Schaum's Probability Outlines) says that A\capB=[-3,8)...

Hi, Thanks for the super detailed response! Yep, I incorrectly copied the question :( I think I understand now

Homework Statement Not exactly a problem, more an example that has me confused :s \frac{dN}{dt}=\kappa N-(\kappa/a^{2})N This describes a population model where N is the population, \kappa is the net births (ie: births less deaths) and it doesn't tell you what a is (this in all the...

Ok awesome, thanks again!

Awesome, thanks! Just to confirm, what's the name of the theorem that states that a subseqence converges to the same limit as the sequence?

Ok, took some time and I had to look at some other examples. Saw something where you let the limit be L and then you solve algebraically, thought I could apply that, so here it goes: I know that u_{2n} is a subsequence of u_{n} where u_{2n}=(a^{n})^{2} I'm not to sure about, but is it...

Ok fair enough. Well, I figured that 0<|a|^{2n}<|a|^{n} by using |a|=\frac{1}{1+h} and then applying bernoullis, which results in that as h must be positive to satisfy the upper bound. From taht I guess you can use standard limits as |a|^{n} converges to 0 by standard limits and so too must...