11. Find Un integer 21). HD w
Let n be a positive integer. For each possible pair i, j of integers with 1<i<i <n, find an n xn matrix A with the property that 1 is an eigenvalue of A with g(1) = i and a(1) = j.
8. Use mathematical induction to prove that n + + 7n 15 3 5 is an integer for all integers n > 0.
Problem 1 (**) Find a positive integer m such that φ(m) < 0.1m.
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
1. Convolution of Discrete Time Signals Analytically determine the convolutions: (a) Find yn]-nun], where un] is the unit step (b) Find yln] z[n] when, where 131 <1
DETAILS LARCALCET7 9.8.042. ASK YOUR TEACHER Find the interval of convergence of the power series, where c> 0 and kis a positive integer. (Be sure to include a check for convergence at the endpoints of the interval. Enter your answer using Interval notation.) (-1***(x-43"
Say that a < 0) and k is a positive integer. Find a constant c such that tk edt < ceżat for all t > 0.
8 otherwise for some constant k. Find: a) the marginal distribution of Y; b) P(Z<}\Y = ). 8. The random variable X has a uniform distribution on (0,1). Given that X = 1, the random variable Y is binomial with parameters n = 5 and p = r. a) Find E(Y) and E(Y?). b) Find P(Y = y and a < X < = + dx). c) Find the density of X given Y = y. Do you recognize it?...
9) Find the absolute maxima and minima of the function f(x,y) = x2 + xy + y2 on the square -8 < x,y 5 8