Find the discrete Fourier approximation \(g_{2}(x)\) for \(f(x)\) based on the table information. \(x |-\frac{\pi}{2} | 0 | \frac{\pi}{2} | \pi\) \(f(x) | 0 | 1 | 3 | -2\)

Find the discrete Fourier approximation \(g_{2}(x)\) for \(f(x)f(x)\) based on the table information. \(x | 0 | \pi\) \(f(x) | 0 | 2\)

If s is a string, define its reverse \(s^R\) as follows. \(\begin{array}{|c|c|}\hline B. & \lambda^R = \lambda \\ \hline R. & \text{If s has one or more symbols, write} \\ & s = ra \\ & \text{where a is a symbol and r is a string (possibly empty). Then} \\ & s^R = (ra)^R = ar^R. \\ \hline \end{array}\) Compute \((cubs)^R\). Justify each step using the definition.

Consider a Poisson process on \([0, \infty)\) with parameter \(\displaystyle\lambda\) and let T be a random variable independent of the process. Assume T has an exponential distribution with parameter v. Let \(N_{T}\) denote the number of particles in the interval \([0, T]\). Compute the discrete density of \(N_{T}\).

is this true or false \({6, {a, b, c}, {b, c, 8}} = {6, {a, b, c}, {b, c, 8}, \not{0}}\)

\(\displaystyle{\left({x}^{{4}}{y}^{{5}}\right)}^{{\frac{{1}}{{4}}}}{\left({x}^{{8}}{y}^{{5}}\right)}^{{\frac{{1}}{{5}}}}={x}^{{\frac{{j}}{{5}}}}{y}^{{\frac{{k}}{{4}}}}\) In the equation above, j and k are constants. If the equation is true for all positive real values of x and y, what is the value of \(j - k\)? A)3 B)4 C)5 D)6

Which of the following are true statements? a:\(2\in\{1,2,3\}\) b:\(\{2\}\in\{1,2,3\}\) c:\(2\subset\{1,2,3\}\) d:\(\{2\}\subset\{1,2,3\}\) e:\(\{2\}\subset\{\{1\},\{2\}\}\) f:\(\{2\}\in\{\{1\},\{2\}\}\)