I am taking my first stats course and struggling quite a bit as my professor does not explain things well. I wanted to double check that I am on the right track. My question is: Show that $f(x)≥0$ for all $x ∈ R$ , where $x$ is the exponential density function:$$f(x) = \begin{cases}λ\operatornam...

Question What are the words to describe the method in the image below? (from Nelsen's Proofs without Words II) Attempt I was thinking and could define the sequence $u_1=2; u_{n+1}=f\circ g^{−1}(u_n)$ where $f(x)=\sqrt x$ and $g(x)=x−2$, as suggested by image, and thus, by the graph, it suggests ...

I am struggling making a cobweb diagram for the function $$x_{t+1}=\dfrac{8x_t}{1+2x_t}.$$ So I understand when making the cobweb diagram, that I have to draw the line $y=x$. But where I have trouble understanding is how to draw the function in the graph. I am given the point $x_0 =0.5$ So I plug...

What is the difference between (probability) and (probability-theory)? If there is none, is it better to use both tags or to decide on one (by tossing a fair coin, of course)?

Almost four years after this discussion, and I think that the current situation is not ideal and we need some rethinking. Users keep tagging with probability-theory questions that should be tagged with just probability. Would it be feasible, eg, to add some warning when people with low reputati...

In Rudin's Principles of Mathematical Analysis (3e), the following exercise is given in the chapter about differentiation: Exr.24 (p.118): The process described in part (c) of Exercise 22 can of course also be applied to functions that map $(0, \infty)$ to $(0, \infty)$. Fix some $\alpha > 1$, a...