Recent content by lveenis

Hi RGV, Thanks for the help! For some reason I had myself convinced that because B and C are mutually exclusive this property wouldn't hold. I see now that it just means P(BC)=0 and P(ABC)=0 since B and C can never happen simultaneously. Again thank you, this helped a lot Luuk V.

Homework Statement This isn't actually a homework question, I'm reviewing for a midterm I have coming up this week and came across this question in some of the practice exercises that were provided. Let A,B,C be three events. Suppose that A and B are independent, B and C are mutually...

That's what I was wondering about, the exponent part. Normally you would just put it into polar form to make the power easy to do. I was curious if there was a way to put it into polar form, or some other trick that I'm unaware of. Thank you for your help, I will try expanding it out and doing...

I'm sorry if this is a stupid question, but I don't understand what you mean exactly?

Homework Statement Let H(ω) be a complex-value function of the real variable ω. For each of the cases below, find |H(ω)| and argH(ω). a: H(ω)= 1/(1+iω)^10 b: H(ω)=(-2-iω)/(3+iω)^2 Homework Equations The Attempt at a Solution Our prof has not taught how to do these types of questions in...

I did yes, my prof was also actually talking about Pascal's triangle in class. I'm just having trouble relating the two I think. Their examples seem to focus around the binomial theorem.

I'm still having some trouble with how the algebra works here :(. I know how to show it using the binomial theorem, but our prof explicitly asks us to prove it without using the binomial theorem. Is there a way to do it using the definition of nCk = n!/(n-k)!k! ?? I tried re-writing the sum of...

Homework Statement Hi everyone, In my assignment I've been asked to show that 2^n = Ʃ(nCi) i from 0 -> n ie: 2^n = nC0 + nC1 + ... + nCn and I have to do this by induction and then also by a combinatorial argument. Homework Equations Right now I'm just working on the induction part...

Thanks for the replies everyone! SammyS, I wasn't sure if that was valid to do, but it seems to give me correct solutions. One note: adding the two gives 3n + 7m = 0 (mod 10). But solving using that equation as you proposed gave me the solutions n = m = 4 and n = m = 9, I'm not sure if you...

I apologize if this is a dumb question, but how do you get the second case? I'm still struggling with this, I know there obviously are solutions because just looking at at n = m = 4 is one possible solution.

We actually went over an example like that in class where we showed at if: ac = bc (mod n) and the gcd(a,n) = 1, then a = b (= meaning congruent) otherwise it's not valid. Correct me if I'm wrong, but in this case c would be 2 and n would be 10, and since those are not relatively prime you can't...

Homework Statement Solver for n and m in the following equations: 2n + 6m \equiv 2 (mod 10) n + m \equiv -2 (mod 10) Homework Equations The Attempt at a Solution I've worked through several of these problems prior, including ones in the book and most take the form: 2n + 3m = 3...