6. Let X have a N(1,2) distribution. Using only the tables, find: a) P(X 1.5) b) P(-1.1 X < 3.3) c) P(X-.9) d) A point c such that P(X > c) = 01 e) A point d such that P(X < d) 005
Let x[n] and y[n] be periodic signals with common period N, and let z[n] = { x[r]y[n – r) r=<N> be their period convolution. Let z[n] = sin(7") and y[n] = { . 0 <n<3 4 <n <7 Asns? be two signals that are periodic with period 8. Find the Fourier series representation for the periodic convolution of these signals.
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
Let n be a positive integer. For each possible pair i, j of integers with 1 sisi<n, find an n x n matrix A with the property that 1 is an eigenvalue of A with g(1) = i and a(1) = j.
Question 25 2 pts Let C be the path from (0,0) to (1, 0) to (1,2). The work done by the force F =< 0,5 > on C is O 10 00 05 O 15
3. Let T = {< M > | m accepts w" when it accepts w. }. Show T is undecidable.
1. Let L = {ambm cn | m <n}. Use the pumping lemma to show that L is not a CFL.
1 4.6.3. (Harder!) Let 0 < a < 1. Prove that for any n EN, (1 – a)” < 1+n·a
Let S = {a, b}. Show that the language L = {w EX : na(w)<n(w) } is not regular.
Let ne Nj. Prove that n < 2(6(n)).