Recent content by zmalone

Homework Statement ΣiYi = 500; ΣiXi = 150; ΣiYi2 = 17000; ΣiXi2 = 4000; ΣiXiYi = 8000; n = 50. β0 = 3. Derive formula for OLS estimator of β1 and find estimateHomework Equations I'm new to OLS and I'm not sure where to go from: Σ(Yi - 3 - b1Xi)^2 I was able to walk through the steps in my...

To redefine the problem more clearly, multiple runs of 3 zeroes are fine (0001234000) and more than 3 zeroes is fine too (1340000023). So essentially the question is what is the probability of getting AT LEAST 1 set of 3 or more zeroes in a row, anywhere in the set of 10 randomly generated...

What would the probability be of 10 randomly generated numbers producing exactly 3 0s in a row at any point in the 10 entries? Ex: 1. 5 2. 0 3. 0 4. 0 5. 9 6. 8 7. 1 8. 0 9. 8 10. 2 Using a binomial distribution to find the probability of any 3 out of 10 I got: 1/10 chance of...

well... So I was just trying to see if there was a trend in this 3x3 subest of the entire matrix which is 266x3 So I guess to rephrase my problem, I will have 266 equations with 3 variables and that is why I want to approximate the variables as close as possible and examine the outliers. Is...

I have a 3 variable system of equations (no solution) and am trying to solve for variables of an Ax = b to be as close to b as possible without changing A. 28446757643x + 82500000y + z = 13557300 283009432x + 283009432y + z = 10264100 14180045548x + 82500000y + z = 3651510 I am...

From the attached image problem: When deriving the third term in the Lagrangian: \lambda_{2}(w^{T}∑w - \sigma^{2}_{\rho}) with respect to w, are w^{T} and w used like a w^{2} to arrive at the gradient or am I oversimplifying and it just happens to work out on certain problems like this? (∑...

I'm watching a lecture on Newton's method with n-dimensions but I am kind of hung up on why the professor did not use the negative sign while taking the first gradient? Is there a rule that explains this or something that I'm forgetting? The rest makes sense but highlighted in red is the part I...

I'm watching a lecture on Newton's method with n-dimensions but I am kind of hung up on why the professor did not use the negative sign while taking the first gradient? Is there a rule that explains this or something that I'm forgetting? The rest makes sense but highlighted in red is the part I...

Wow :( I don't know why I was taking the derivative of 1 instead its anti-derivative but I certainly confused myself by doing so for the past half hour. Thanks for pointing it out!

I understand \int^{1}_{-1}1-|x|dx = 1 visually just by graphing it and taking the area of the triangle but for the sake of more complicated examples I'm not exactly sure what step I'm messing up when I use the FTOC: |x|= x when x>0, -x when x<0 \int^{0}_{-1}1-|x|dx + \int^{1}_{0}1-|x|dx...