Recent content by TheEmptySet

Maybe I am misunderstanding something but the way I read the problem was if we have the data set $\{0,2 \}$ we can calculate the mean and variance directly. Now if a new data set is created by adding one other point $\{0,2,y \}$. We can now calculate the new population mean and the new...

The variance is the square root of the sum of the differences from of the data points from the mean so... $\sigma^2=\frac{1}{2}\left[(0-1)^2+(2-1)^2\right]=1$. If we add the new point $y$, we will need to solve the system of equations. $\mu=\frac{1}{3}\left[ 0+2+y\right]$ and...

Re: Area

I thought of this in terms of linear algebra and vector spaces. Consider the set \begin{matrix} g_0(x)=\sqrt{c_0} & g_0^2(x)=c_0 \\ g_1(x)=(1+c_1x) & g_1^2(x)=1+2c_1x+c_1^2x^2\\ g_2(x)=\sqrt{c_2}x & g_2(x)=c_1x^2\\ g_3(x)=(x+\sqrt{c_3}x^2) & g_3(x)=x^2+c_3x^3+c_3^2x^4\\ g_4(x)=\sqrt{c_4}x^2)...

I used this book Partial Differential Equations of Mathematical Physics and Integral Equations (Dover Books on Mathematics): Ronald B. Guenther,John W. Lee,Mathematics: 9780486688893: Amazon.com: Books It is in its dover days now, but I quite liked it. It is very inexpensive

Think about the idea behind the method of characteristics. We start by parameterizing the independant variables x and y. x=x(s,t) \quad y=y(s,t) \implies u(x,y)=u(x(r,s),y(r,s)) Now take the derivative with respect to s to get...