Recent content by Proggy99

I did some poking around trying to find hints but can not seem to find any beyond proving uniqueness for the division algorith for real numbers. I can not seem to find a way to apply a similar method here. Help please.

Homework Statement Theorem Let \alpha\neq0 and \beta be Gaussian integers. Then there are Gaussian integers \tau and \rho such that \beta=\tau\alpha+\rho and N\left(\rho\right)<N\left(\alpha\right) Problem Show that the Guassian integers \tau and \rho in the Theorem are unique if and only...

hmmmm, so a/(a^2+b^2) can only be an integer if a^2+b^2 is a, 1 or -1, but b/(a^2+b^2), implies that a^2+b^2 is b, 1 or -1. Therefore, a^2+b^2 must equal 1 or -1. For that to be true, then either a^2=1 and b^2=0 or a^2=0 and b^2=1. Then a=1 or -1 and b=0 or b= 1 or -1 and a =0. Plugging...

by the way, I am wondering why this does not work for an explanation? a+bi = i(b-ai) and b-ai is another Gaussian integer, so any a+bi is a multiple of i. a+bi = -i(-b+ai) and –b+ai is another Gaussian integer, so any a+bi is a multiple of -i. a+bi = 1(a+bi), so any a+bi is a multiple of 1...

okay, the concepts here are being stubborn about not sinking in. By multiplying complex conjugates, I believe you mean (a+bi)(a-bi)= a^{2}-i^{2}b^{2}=a^{2}+b^{2} So 1/(a+bi) * (a-bi)/(a-bi) = (a-bi)/(a^{2}+b^{2}) so then (a-bi)/(a^{2}+b^{2}) = a/(a^{2}+b^{2})-(b/(a^{2}+b^{2}))i which is a...

Thank you for that. Your explanation led me back to the previous section where they covered a+bi Gaussian integers and the very last sentence of the section made the comment that Gaussian integers were represented by Z[i]. I already proved in the previous section that a+bi = i(b-ai) and that...

This is my first assignment in my Modern (Abstract) Algebra class, just to give an idea where I am with tools that I can use. Homework Statement Describe all units and zero divisors in Z[i] Homework Equations The Attempt at a Solution I already know the answers are units = 1...

it means that P(max(X,Y) \leq t) = P(X \leq t)P(Y \leq t) = F*G yes, no, maybe? this part for min(x,y) i am pretty sure was wrong, so looking into it more.

I am really struggling with the material since the midterm, so I am not sure I know what you are asking. Are you referring to H(t) = P(X \leq t) ?

Homework Statement Let X and Y be two independent random variables with distribution functions F and G, respectively. Find the distribution functions of max(X,Y) and min(X,Y). Homework Equations The Attempt at a Solution Can someone give me a jumping off point for this problem...

gah, thanks for the catch. Looking past that, I realized I had consistently added rather than subtracted when doing my integration by parts, so I did the sign wrong three times resulting in a change in the final answer from negative to positive. Thanks for pointing it out.

Homework Statement Let the join probability density function of ZX and Y be given by f(x,y)=\left\{\stackrel{2e^{-(x+2y)}\ \ \ \ \ if\ x\ \geq,\ \ \ y\ \geq\ 0}{0\ \ \ \ \ \ \ otherwise} Find E(X^{2}Y) Homework Equations I approached this problem using a theorem from the book that states...

Well, I know that the expected value is the mean, or average, of the possible answers. I also know that xcosx creates a graph that is symmetrically when turned at a 180 degree angle around 0. This tells me that there are positive and negative values that offset each other leaving the answer to...

I took the calculus series as a freshman in college 19 years ago. I am struggling through a few higher level courses in my pursuit of a 7-12 integrated mathematics teaching degree. This homework is for an advanced statistics and probability class through independent study at LSU. I have...

Ahhh, that makes perfect sense statdad. I kept trying to factor out 'x' when I looked at it the way you did it and got nowhere so discarded that method. I would substitute that with the equation I put in my first post to get the equation from the definition of positive normal. I just could not...