Recent content by sid9221

Suppose we have a function V(x,y)=x^2 + axy + y^2 how do we write \frac{dV}{dt} For instance if V(x,y)=x^2 + y^2, then \frac{dV}{dt} = 2x \frac{dx}{dt} + 2y \frac{dy}{dt} So, is the solution \frac{dV}{dt} = 2x \frac{dx}{dt} + ay\frac{dx}{dt} + ax\frac{dy}{dt} + 2y \frac{dy}{dt}

I'm trying to show that E[x_i]=\bar{X} where \bar{x} is the sample mean and \bar{X} is the population mean

I'm having a little trouble with the proof that the expected value of x_i is \bar{X} What I have is E[x_i]=\sum_{j=1}^{N}X_j Pr(x_i=X_j) Then Pr(x_i=X_j) = 1/N This is the bit I can't understand, how does that probability evaluate to that value. I know the denominator...

Hi, I can't come up with a general forumla for x in this equation. Any advice ? x = y sin(x)

μ=\frac{\sum X_i}{N} x_1 is just a variable

Where is this defined ? Is is part of the definition of 'Expectation' ?

I don't completely understand why the area of the proof circled in red is true. Any advice would be appreciated. https://dl.dropboxusercontent.com/u/33103477/Q1.jpg

What do you mean normalize to 1 ? It was 7/2k=1 So k=2/7 ?

A continuous random variable X has pdf: f_X(x)=\left \{ k(x+3), 0\leq x\leq 1\right \} 0 otherwise. Find k. I solved the integral (from 0..1) and solved for the result equal to 1. Hence I got k=2/7. Is this the right way to proceed as the question continues and I want to check if I'm...

I evaluated a few terms during the exams(beginning with 1) its not a little bigger it's ALOOOT bigger. So much so that you can't evaluate beyond r=13 as size of the number is too big. At r=14 there are more digits in the result than atoms in the universe so it kinda goes without saying that...

It was in my exam, it's already over. I did the ratio test for some reason cut it out and put this instead as it was smaller. It's correct right ?

\sum_{r=1}^{\infty} \frac{r!}{3^{r^{2}}} My solution: \frac{3^{r^2}}{r!} > r^2 So \frac{r!}{3^{r^2}} < \frac{1}{r^2} So as 1/r^2 converges, it converges by comparison test. This was in my exam today, I messed up a lot leading up to it. But the question said I could use any test in...

I think by dimension you mean "nullity" cause our lecturer also used "dimension of a matrix" which was confusing when studying from other sources. Try plugging your matrix in wolfram and ask for nullity. In the output it states a "dimension" which is always exactly what I always needed. So...

Guy's this is a past exam paper question and it has come up twice. If it was a mistake it wouldn't have come up two times in exactly the same form. On a side note this has come up in the sequences portion of the paper(we have separate sections for different topics on the paper's easier bit)...

Easy way to remember it is: # of columns - # of non zero rows in rref