P.5 Find the power of the periodic signal x(1) shown below. x(1) 3 2 4/3-241 1 13 4 -2 -3
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- suppose that alpha(t) = 12t^2-6,with v(0) = 5 and s(0) = 10 find s(t) and graph alpha(t), v(t) and s(t)b. Find a formula for A−1(t) for the values of t for which A(t) is invertible. (see image)The grades on a history midterm at Santa Rita are roughly symmetric with \mu = 76μ=76mu, equals, 76 and \sigma = 3.0σ=3.0sigma, equals, 3, point, 0. Ben scored 717171 on the exam. Find the z-score for Ben's exam grade. Round to two decimal places.
- If the moment generating function of X is M(t)= 0.2+0.3(e^-t)+0.5(e^3t), then P(X>-1)=10. Suppose is a periodic function with period 11. What is the smallest period possible for the multivariate function and in what direction does it occur?Suppose that Xi ∼ Gamma(αi , β) independently for i = 1, . . . , N. The mgf(moment generating function) of Xiis MXi(t) = (1 − (t/β) )−αi . (a)Use the mgf of Xi to derive the mgf of ∑i=1 Xi . Use the mgf of Xi to derive the mgf of ∑i=1 Xi
- 1. Solve the following points based on the periodic function shown in the attached image: a) Draw the graph of the function. b) obtain the trigonometric fourier series representation of f(t).2. find the fourier coefficients for the function of period 2pie as follows: f(t)=2t^3,- pie<t<pie2. Consider an ODE of the form:x2y′′+axy′+by = 0 with given constants a and b and unknown solution y(x). Assuming that y(x) follows the form y=xm, perform the following tasks:a.) Solve for y′(x) and y′′(x) and transform the given ODE in terms of x,m,a, and b.b.) Determine the characteristic equation of the ODE.