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Part II. Sec. 4.4. Consider the alphabet {x,y,z). Let In be the number of words of...
(a) An alien species communicate using the alphabet (x, y,zIn their language, words must obey one...
Discrete Math
(a) An alien species communicate using the alphabet (x, y,zIn their language, words must obey one single rule: zz cannot be part of the word, otherwise the speaker will go to sleep and never finish the sentence. How many words of length n exist in this language? Hint: Use a recurrence, by considering all possibilities for the first letter of the word
(a) An alien species communicate using the alphabet (x, y,zIn their language, words must obey one...
Consider binary strings with n digits (for example, if n = 4 some of the possible...
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.) Let z be the number of binary strings of length n that do not contain the substring 000 Find a recurrence relation for z You are not required to find a closed form for this recurrence
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.)...
(6) (a) Consider the follow ing graph U T S 1] (ii) Does the graph have...
(6) (a) Consider the follow ing graph U T S 1] (ii) Does the graph have a closed Euler trail? If so, give an example of a closed Euler trail in 2] 1] (iv) Two identical looking bags are on a table. One cont ains 30 green marbles and 30 black marbles, and the other contains 10 green marbles, 10 blue marbles and 10 red marbles One of the bags is randomly selected (each has a 50% chance of being...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
Question 1 、 Let X, Y and Z be three random variables that take values in the alphabet {0,1, M-l...
Question 1 、 Let X, Y and Z be three random variables that take values in the alphabet {0,1, M-lj. We assume X and Z are independent and Y = X +2(mod M), The distribution of Z is given as P(Z 0)1 -p and P (Z =i)= , for i = 1, M-1. For question 1-3 we M-1 will assume that X is uniform on f0,1,..,M-1}. Find H(X) and H(Z) Find H(Y ) Find 1 (X; Y) and「X, YZ) and...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings of length n which do not contain AA or BA as substrings. Find a recurrence for tn, and then use that to find a closed-form (i.e. non-recursive) formula for tn.
Let S1 be the part of the paraboloid z = 1 − x ^2 − y...
Let S1 be the part of the paraboloid z = 1 − x ^2 − y ^2 that lies above the plane z = 0. Let S2 be the part of the cone z = √ x ^2 + y ^2 + 2(sqrt till y^2) that lies inside of the cylinder x ^2 + y^ 2 = 1. Let S3 be the part of the cylinder x ^2 + y ^2 = 1 that lies between these surfaces. If S...
(c) Let F be the vector field on R given by F(x, y, z) = (2x...
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
Block Walking and Counting Subsets A Delannoy path in the first quadrant is a walk that uses any of 3 kinds of steps: Up (0,1), Right (1,0), and Diagonal (1, 1). Let D(x, y) be the number of Delannoy...
Block Walking and Counting Subsets A Delannoy path in the first quadrant is a walk that uses any of 3 kinds of steps: Up (0,1), Right (1,0), and Diagonal (1, 1). Let D(x, y) be the number of Delannoy paths from (0,0) to (x, y). (a). Find a recurrence relation that gives D(x, y) in terms of smaller values. (b). Find the number of Delannoy paths from (0, 0) to (7,3) c). Find a formula for D(n,1), where n is...
Need help with this question. Thank you :) (6) (a) Consider the following graph P R...
Need help with this question. Thank you :)
(6) (a) Consider the following graph P R U T (i) What are the degrees of the vertices in the graph? (ii) Does the graph have a closed Euler trail? If so, give an example of a closed Euler trail in the graph. If not, explain why no closed Euler trail exists. (iii Give an example of a spanning tree in the graph (iv) Two identical looking bags are on a table....
Discrete Math
(a) An alien species communicate using the alphabet (x, y,zIn their language, words must obey one single rule: zz cannot be part of the word, otherwise the speaker will go to sleep and never finish the sentence. How many words of length n exist in this language? Hint: Use a recurrence, by considering all possibilities for the first letter of the word
(a) An alien species communicate using the alphabet (x, y,zIn their language, words must obey one...
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.) Let z be the number of binary strings of length n that do not contain the substring 000 Find a recurrence relation for z You are not required to find a closed form for this recurrence
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.)...
(6) (a) Consider the follow ing graph U T S 1] (ii) Does the graph have a closed Euler trail? If so, give an example of a closed Euler trail in 2] 1] (iv) Two identical looking bags are on a table. One cont ains 30 green marbles and 30 black marbles, and the other contains 10 green marbles, 10 blue marbles and 10 red marbles One of the bags is randomly selected (each has a 50% chance of being...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
Question 1 、 Let X, Y and Z be three random variables that take values in the alphabet {0,1, M-lj. We assume X and Z are independent and Y = X +2(mod M), The distribution of Z is given as P(Z 0)1 -p and P (Z =i)= , for i = 1, M-1. For question 1-3 we M-1 will assume that X is uniform on f0,1,..,M-1}. Find H(X) and H(Z) Find H(Y ) Find 1 (X; Y) and「X, YZ) and...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings of length n which do not contain AA or BA as substrings. Find a recurrence for tn, and then use that to find a closed-form (i.e. non-recursive) formula for tn.
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
Block Walking and Counting Subsets A Delannoy path in the first quadrant is a walk that uses any of 3 kinds of steps: Up (0,1), Right (1,0), and Diagonal (1, 1). Let D(x, y) be the number of Delannoy paths from (0,0) to (x, y). (a). Find a recurrence relation that gives D(x, y) in terms of smaller values. (b). Find the number of Delannoy paths from (0, 0) to (7,3) c). Find a formula for D(n,1), where n is...
Need help with this question. Thank you :)
(6) (a) Consider the following graph P R U T (i) What are the degrees of the vertices in the graph? (ii) Does the graph have a closed Euler trail? If so, give an example of a closed Euler trail in the graph. If not, explain why no closed Euler trail exists. (iii Give an example of a spanning tree in the graph (iv) Two identical looking bags are on a table....
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