Sorry I have no idea how to do that! I'm not sure I've ever been taught it. Though obviously it is necessary to do this question! Could you explain how, please, or point me in the direction of somewhere that can? Thanks very much!
Homework Statement
I need to show that two elements in \textbf{Z}[\sqrt{-5}] have gcd = 1.
The elements are 3 and 2+\sqrt{-5}
Homework Equations
The Attempt at a Solution
My way of thinking was if I can show that both elements are irreducible, then they are both prime and hence...
OK I´ve managed to get slightly further on this..I think. I'm afraid you'll have to bear with the lack of Latex, as this computer I am at now doesn´t support it for some reason.
So I found the pdf to be
f_X(x) = 0 if x<1
1/10 if 1<=x<3/2
1/3 if 3/2<=x<5/2
0 if...
Yes. I think that may be the point of the question. Does it mean I can´t do it then? As the next part of the question asks me to split up the F_Y into the discrete and continuous parts- ie F = \lambdaF_1 +(1-\lambda)F_2
Which means it probably isn't continuous in the first place...?
Thanks.
Homework Statement
I have been given the distribution function F_X of the random variable X and I am asked to find the distribution function F_Y of Y, another random variable which is defined from X in the following way.
Y={\stackrel{X^{2} if X<2;}{4 if 2\leq X < 3;}\stackrel{4(4-X) if...
Homework Statement
Hello, I just want to know if I am going about this the right way.
A and B are outcomes of a random experiment in a sample space \Omega such that \Omega = A\cupB. P(A) = 0.8 and P(B) = 0.5 Study if A and B, A and B^{c}, A^{c} and B, and A^{c} and B^{c} are independent...
Homework Statement
Hello, I don't entirely understand the question here. It is the limit of a sequence, however it is defined on what appears to be an interval, and is different if n is odd or even. Excuse the messy notation here, I don't know how to use LaTeX.
Let the sequence {A_n : n>=1}...