# functions's questions - English 1answer

19.793 functions questions.

### -1 Carrying an integral to a specific value of the integrand via parametrized weight function

0 answers, 20 views calculus integration limits functions
Let's say I have an integral $\int_0^1 f(t)dt$, being $f$ a continuous real function, and I add a continuous weight function $h(s,t)$ depending on a parameter $s\in[0,1)$, with the intention of ...

### 1 Point-free notation for function composition?

1 answers, 31 views functions notation
Let $f$ and $g$ be a pair of functions mapping reals to reals. It is common to use the point-free notation $f\circ g$ to describe the function $h$ defined by $h(x)$ = $f(g(x))$. By "point-free" I mean ...

### 4 Continuous function on $[0,1]$, $f(0)=f(1)$

1 answers, 43 views general-topology functions continuity

### -2 The probability that that does not contain two consecutive numbers is equal to [on hold]

Of all the subsets of {1,2,3,4,5,6,7} a non-void subset is randomly selected. The probability that it does not contain two consecutive numbers is equal to

### 1 What choices of $c, d$ would make $\int_{x=-\infty}^{x_0} (cx - d) \mathcal{N}(x; \mu, \sigma^2)\,dx$ positive?

Consider the following integration: $$I(x_0|c, d) = \int_{x=-\infty}^{x_0} (cx - d) \mathcal{N}(x; \mu, \sigma^2) \,dx$$ In this notation, $\mathcal{N}(x; \mu, \sigma^2)$ is a normal distribution: ...

### 3 Sequential maximization $\max_{x} \max_{y} f(x,y)$ vs. simultaneous maximization $\max_{x,y} f(x,y)$

Let $f(x,y)$ be a non-separable, non-negative real-valued function, that is jointly concave in $x$ and $y$. We want to maximize $f(x,y)$ over $x$ and $y$. Is the sequential maximization \max_{x} \...