Jan 22, 2017 · 2) x^{-a}=1/{x^a}-- so when a = 0, x^{-0} = 1/x^0 = x^0, which again does work for 0^0 = 1; 3) {x^a}^b = x^{a×b}, thus x^(1/n) is the n-th root -- and 1/n = 0 for no value of n, so …

Aug 25, 2012 · That's why you set the equation to 0 and not any other number; to find the X-intercept(s) aka (x, 0) point(s). The ROOTS of a quadratic equation exactly means the x …

x 0 1 2 P(x) 0.4 0.4 0.2 The team plays 2 games. The number of home runs scored in one game is independent of the number of home runs in the other game. Let Y be the total number of …

SOLUTION: Help Needed; Use graphical methods to solve the linear programming problem. Maximize z = 6x + 7y subject to: 2x + 3y ≤ 12 2x + y ≤ 8 x ≥ 0 y ≥ 0

May 19, 2021 · Let $(X_n)_{n \geq 1}$ be a sequence of independent random variable such that $\mathbb{P}(X_n = 0) = 1 - \frac{1}{n^2}$ and $\mathbb{P}(X_n = n^3)=\frac{1}{n^2}$.

Sep 18, 2024 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Mar 10, 2016 · Observe that for a continuous random variable, (well absolutely continuous to be rigorous): $$\mathsf P(X> x) = \int_x^\infty f_X(y)\operatorname d y$$

Note that $$\frac{1}{1+x}=\sum_{n \ge 0} (-1)^nx^n$$ Integrating both sides gives you \begin{align} \ln(1+x) &=\sum_{n \ge 0}\frac{(-1)^nx^{n+1}}{n+1}\\ &=x-\frac{x^2 ...

SOLUTION: A circle is circumscribing a triangle formed by the lines y=0, y=x and 2x+3y=10. Find the equation of the circle

$$\sin x<x\,(0<x<\frac{\pi}{2})$$ In most textbooks, to prove this inequality is based on geometry illustration (draw a circle, compare arc length and chord ), but I think that strict proof should be …