The following problem is from Devore's Probability and Statistics for Engineering and the Sciences, 8th edition, exercise 8.1 question 33:
Reconsider the accompanying sample data on expense ratio(%) for large-cap growth mutual funds first introduced in Exercise 1.53:
I cannot figure...
@Masterphile $R(A\cap B)=R(A)\cap R(B)$ for all $A,B$ is equivalent to $xRy\land x^{\prime}Ry\Rightarrow x=x^{\prime}$ for all $x,x^{\prime},y$ (this is well-known for $R$ a function)
@Masterphile the thing is that this injectivity-like condition really only has to do with the equality when we consider $A,B$ as singletons, I don't think there's an easier characterization if you just look at arbitrary sets
nah, try with this: 1+1/2+...+1/n - ln(n) is irrational for every n, henceforth, the limit, euler-mascheroni constant is irrational as it is the limit of only irrational numbers @geocalc33
Since every irrational number can be approximated with rationals, and rationals are everywhere dense, is it true that every rational is dense in the $\mathbb R^n$, with the usual metric?
I'm a bit confused as to how the ${2n}^C_{n}$ corresponds to getting back to the origin after $2n$ steps. It's been a while since I did any discrete stochastic, @Simple.
The following problem is from Devore's Probability and Statistics for Engineering and the Sciences, 8th edition, exercise 8.1 question 33:
Reconsider the accompanying sample data on expense ratio(%) for large-cap growth mutual funds first introduced in Exercise 1.53:
I cannot figure...
Consider some piecewise maps from $\Bbb R^2\to \Bbb R^2$
$$f(x_1, x_2) = (e^{x_1}, e^{x_2}).~~~~~x_1,x_2 \le 0$$
$$ g(x_1, x_2) = (e^{-x_1}, e^{-x_2})~~~~~~ x_1,x_2 \ge 0$$
$$ h(x_1,x_2)= (-e^{-x_1}, -e^{-x_2})~~~~~~x_1,x_2\ge0$$
$$ j(x_1, x_2) =(-e^{x_1}, -e^{x_2}). ~~~~~x_1,x_2 \le 0$$
Thes...
