Recent content by mliuzzolino

Doh! That little fact completely slipped my mind. Thanks guys!

Homework Statement A random variable has a Poisson distribution with parameter λ = 2. Compute the following probabilities, giving an exact answer and a decimal approximation. P(X ≥ 4) Homework Equations P(X = k) = λke-λ/k! The Attempt at a Solution P(X ≥ 4) = Ʃk = 4∞...

Ah. I have it figured out now. I can't believe I overlooked such an elementary concept... Thank you Ray!

My mistake in the previous reply to you. The expression should be \vec{k} \cdot S \cdot \vec{k}^T . Let \vec{k} be a 1 x N matrix and S an N x N matrix. The dot product of S and \vec{k}^T will result in an N x 1 matrix which is then dotted with the 1 x N \vec{k} matrix, resulting in a scalar.

Unfortunately, my result does not seem to match with the solution arrived at in the paper which is provided in 2. Homework Equations .

Sorry! I forgot to state that S is a symmetric positive definite matrix. I believe that the operation will just be taking the dot product of \vec{k} and S, and then using that as the scalar weight on \vec{k} . This is for a research project and I'm just going through old literature trying...

Homework Statement For a Gaussian landscape, the log-fitness change caused by a mutation of size r in chemotype element i is Q_i(r) = -\vec{k} \cdot S \cdot \hat{r_i}r - \dfrac{1}{2} \hat{r_i} \cdot S \cdot \hat{r_i}r^2 . To find the largest possible gain in log-fitness achievable by...

Ok. I see where I'm going wrong with this idiotic summation stuff. I don't know what I was thinking.

Would it be... S(n) = \sum_{j = 2}^{n} j - 1 = 1 + 2 + \cdots + (n - 1) = \dfrac{n(n - 1)}{2} S(2) = (2 - 1) = 1 = \dfrac{2(2-1)}{2} = 1 ?

Homework Statement Prove that if n is a natural number greater than 1, then n-1 is also a natural number. (Hint: Prove that the set {n | n = 1 or n in \mathbb{N} and n - 1 in \mathbb{N} } is inductive.)Homework Equations The Attempt at a Solution S(n) = \sum_{j = 2}^{n} j = 2 + 3 + \cdots...

That makes a lot of sense. I appreciate it both of you!

Homework Statement The moment generating function (m.g.f.) of a random variable X is defined as the Expected value of etX: M(t) = E(etX). The series expansion of etX is: etX = 1 + tX + (t2X2)/(2!) + (t3X3)/(3!) + ... Hence, M(t) = E(etx) = 1 + tμ1' + (t2μ2')/2! + (t3μ3')/3! +...

I suppose that I wasn't clear in what I meant. I meant that the knowledge acquired and/or the opportunities it will open for personal gain far outweigh saving $20k. My point being that finance isn't a factor in my decision, so I'm hoping for responses void of the "financial gains" component...

Hey everyone! Well, I am entering what would be my senior year at the University of Arizona where I am double majoring in Applied Mathematics and Molecular & Cellular Biology. I plan to pursue a Ph.D. (and beyond) and have been engaging in activities that will make me more competitive for...

I apparently need to familiarize myself more with hyperbolic functions! I should have assumed there was some trick like this. Thanks a lot for your help! It all makes sense now. :)