Recent content by Catchfire

So after some integration with polar coordinates refreshing the limits should have been something like pi to 3/2pi and 0 to infinity. This however would have left me with my centre at the origin not (0.5, 0.5). Which is why when I integrate from the origin I get 0.5 which is less than 0.6915...

So that's what all those tables in the back of my text are for, lol. I guess the text I'm using assumes some level of familiarity with these tables as I haven't seen them mentioned yet. Well that makes things much easier. Still it's much more satisfying to work the problem than look it up. In...

Ahh yes I see. That's a very handy property I would suspect, thanks. So I was getting the impression I was going to have to solve this with the error function (which isn't mentioned in my text... or at the very least it's not in the index and I haven't come across it yet). So are you saying...

Sorry I think you miss read my post. The minus sign almost looks like a dot if not in latex tags. I've edited the original post to clarify things.

Can you elaborate? How does P(X>10) = P(X<0)? Also both of you mention changing the limits when going from Cartesian to Polar. I'm guessing going to polar coordinates isn't the right method since we're dealing with a rectangular area.

Yeah I had a feeling that's where the issue was. Thanks, I wasn't sure if it would work but I'd already tried integration by parts and that didn't seem to be going in the right direction. Guess I should scrap this solution. And yes you're right, it should be X~N(5,100), at least...

Homework Statement Let X ~ norm(5,10). Find P(X>10).Homework Equations f(x) = \frac{1}{δ\sqrt{2π}} e^{-\frac{(x-μ)^2}{2δ^2}} F(x) = P(X<x) = \int_{-∞}^x f(u) du The Attempt at a Solution P(X>10) = 1 - P(X<10) P(X<10) = \int_{-∞}^{10} \frac{1}{δ\sqrt{2π}} e^{-\frac{(x-μ)^2}{2δ^2}} dx =...

Looks like I need to refresh myself on the laws of exponents. That substitution did the trick, thanks.

Homework Statement Show the gamma density function integrates to 1.Homework Equations Assume α > 0, λ > 0, t > 0 g(t) = \frac{λ^α}{\Gamma (α)} t^{α-1}e^{-λt} \Gamma (α)= \int_0^∞ t^{α-1} e^{-t} dt The Attempt at a Solution Show \int_0^∞ \frac{λ^α}{\Gamma (α)} t^{α-1}e^{-λt} dt = 1...

Homework Statement From Mathematical Statistics and Data Analysis 3ed, Rice 1.8 #61 Suppose chips are tested and the probability they are detected if defective is 0.95, and the probability they are declared sound if they are sound is 0.97. If 0.005 of the chips are faulty. What is the...

Thanks. Ps sorry mods, posted in wrong forum, please move to homework subforum.

Hello, I've been working on some questions from Rice's Mathematical Statistics and Data Analysis and I'm not sure about my solutions. The question I'm working on is as follows: 1.8 #59c A box has 3 coins: 1 with two heads, 1 with 2 tails and 1 fair coin. A coin chosen randomly is flipped...

Thanks for the responses, I appreciate the help.

Nothing, but I already know the answers to the problem. I just wanted to make sure my reasoning was correct and that I understood what theorem voko was citing. Can you lend a hand with any of that? It would much appreciated if you could.

So are you saying dim(A) = rank(A) + nullity(A) and since dim(A-I) = 3 and rank(A-I) = 1, then nullity(A-I) = 2, implying I need two vectors from A-I.Ahh I see where I messed up, since there is no y values I can write y = a for any a in R. So really my eigenvectors are (1,a,1) and (0,b,0). Is...