random walk - Hi I would appreciate if you could help me with this question. Is the question below TRUE or FALSE and explain why ? Question: I have two random walks, both starting at 0 and with a reflecting boundary at 0. Each Step, Walk A goes up 1 with probability 1/2 and down 1 with probability 1/2(except at the boundary). Each step, Walk B goes up 1 with probability 1/3 and down 1 ...

Prime numbers - 6301 is prime. If x, y, and z are integers that are not divisible by 6301, which of the following is equal to x^6299.y^12600.z^18903 mod 6301 ? (a) xyz (b) yz2/x2 (c) z3/x (d) 1/(x2 y2) (e) none of the above

network flow - Hi Consider any graph G with edge capacities, a source s, and a sink t. Suppose the maximum flow from s to t is greater than 0, so there is a path from s to t. Then there always exists an edge so that increasing the capacity on the edge increases the maximum flow from s to t. Is Answer True or False Thanks

Primality - Which of the following is true. a) 16 is a non-trivial square root of 1 modulo 51; hence 51 is composite b) 7 is a non-trivial square root of 1 modulo 47; hence 47 is composite c) 8 is a non-trivial square root of 1 modulo 55; hence 55 is composite d) all of the above e) None of the above

Travelling salesman problem - Hi It's a TRUE or FALSE question. Please say if this is True or False and why why. Question: =================== The planar 2-approximation algorithm for the Travelling salesman problem will also work in three-dimentional space. ===================