In a normally distributed variable, a value x∗ is considered unusually large if (A) P (x ≤ x∗) < 0.05. (B) P (x ≥ x∗) < 0.05. (C) P (x ≤ x∗) > 0.05. (D) P (x ≥ x∗) > 0.05. (E) P (x = x∗) > 0.05.
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- Consider the (directed) network in the attached document We could represent this network with the following Prolog statements: link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Now, given this network, we say that there is a "connection" from a node "X" to a node "y" if we can get from "X" to "Y" via a series of links, for example, in this network, there is a connection from "a" to "d", and a connection from "c" to "f", etc.Prolog Consider the (directed) network in the attached document. We could represent this network with the following Prolog statements: link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Now, given this network, we say that there is a "connection" from a node "X" to a node "Y" if we can get from "X" to "Y" via a series of links, for example, in this network, there is a connection from "a" to "d", and a connection from "c" to "f", etc. Formulate the appropriate Prolog rule "connection(X,Y)" which is true if (and only if) there is a "connection" from "X" to "Y" as described above --- note that this rule will be recursive. Test this rule out on the above network, to see if it is working correctly. Once it is working correctly, you will note that, e.g., the query "connection(a,e)." will give "true" multiple times. This means something, actually:Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) T[i, j] = ( T[i − 1, j] or T[i, j − ci]) b) T[i, j] = ( T[i − 1, j] and T[i, j − ci ]) c) T[i, j] = ( T[i − 1, j] or T[i − 1, j − ci ]) d) T[i, j] = ( T[i − 1, j] and T[i − 1, j − cj ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) T[1, K + 1] b) T[n, K] c) T[n, 0] d) T[n, K + 1]
- Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) ?[?, ?] = ( ?[? − 1, ?] ?? ?[?, ? − ?? ]) b) ?[?, ?] = ( ?[? − 1, ?] ??? ?[?, ? − ?? ]) c) ?[?, ?] = ( ?[? − 1, ?] ?? ?[? − 1, ? − ?? ]) d) ?[?, ?] = ( ?[? − 1, ?] ??? ?[? − 1, ? − ?? ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) ?[1, ? + 1] b) ?[?, ?] c) ?[?, 0] d) ?[?, ? + 1]Consider a system that handles railway connections as it associates (source) cities to all their corresponding destinations. The requirements of the system are as follows: 1. A source city may have connections to possibly multiple destination cities. 2. Multiple source cities may share the same group of destination cities. We introduce type CITY . A possible state of the system is shown below as it is captured by variable connections:connections ={Montreal → {Ottawa, Kingston, Quebec, Halifax},Ottawa → {Montreal, Toronto},Toronto → {Montreal, Ottawa},Halifax → {Montreal, Quebec},Quebec → {Montreal, Halifax},Kingston → {Montreal}} 1. Is connections a binary relation? Explain why, and if so express this formally. 2. In the expression connections ∈ (...), what would the RHS be? 3. Is connections a function? If so, define the function formally, and reason about the properties of injectivity, surjectivity and bijectivity. 4. Describe the meaning and evaluate the following…A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.
- What is the time and space complexity of this function? It is a dfs function which goes through every possible path from node to another without cycles. Time complexity could be either O(n!) or O(2^n), or is there another answer? What is the space complexity? def dfs(currency_pairs, source, target): graph = defaultdict(dict) for s1, s2, rate_val1, rate_val2 in currency_pairs: graph[s1][s2] = rate_val1 graph[s2][s1] = rate_val2 def backtrack(current, seen): if current == target: return 1 product = 0 if currentingraph: neighbors = graph[current] for neighbor in neighbors: if neighbor not in seen: seen.add(neighbor) product = max(product, graph[current][neighbor] * backtrack(neighbor, seen)) seen.remove(neighbor) return product return backtrack(source,…Consider the Omega network and Butterfly network from p nodes in the leftmost column to p nodes in the rightmost column for some p=2^k. The Omega network is defined in Chapter 2 of the text book such that Si is connected to element S j if j=2i for or j=2i+1-p for See Chapter 2 in text book for its definition. The Butterfly network is an interconnection network composed of log p levels (as the omega network). In a Butterfly network, each switching node i at a level l is connected to the identically numbered element at level l + 1 and to a switching node whose number differs from itself only at the lth most significant bit. Therefore, switching node Si is connected to element S j at level l if j = i or j . Prove that for each node Si in the leftmost column and a node Sj in the rightmost column, there is a path from Si to Sj in the Omega network. Prove that for each node Si in the leftmost and a node Sj in the rightmost, there is a path from Si to Sj in the Butterfly network.implement program to Finding the Longest Common Substringproblem that lends itself to a dynamic programming solution is finding the longest common substring in two strings. For example, in the words “raven” and “havoc”, the longest common substring is “av”.
- Describe an efficient algorithm for finding a maximum spanning tree in G, which would maximize the bandwidth between two switching centers. Describe the problem in terms of input and expected output clearly. Develop a program that accepts a network G of switching centers and the bandwidth between them (not all are connected directly with each other) and two switching centers a and b; it will output the maximum bandwidth between any two switches a and b. Please give solution in Java/C/Python languageIn this problem, let REF(x.i) → DEF(x.k) denote that the linker willassociate an arbitrary reference to symbol x in module i to thedefinition of x in module k . For each example below, use thisnotation to indicate how the linker would resolve references to themultiply-defined symbol in each module. If there is a link-time error(rule 1), write " ERROR ". If the linker arbitrarily chooses one of thedefinitions (rule 3), write " UNKNOWN ".A./* Module 1 */ /* Module 2 */int main() static int main=1[{ int p2()} {}(a) REF(main.1) → DEF(_____._____)(b) REF(main.2) → DEF(_____._____)B./* Module 1 */ /* Module 2 */int x; double x;void main() int p2(){ {} }(a) REF(x.1) → DEF(_____._____)(b) REF(x.2) → DEF(_____._____)C./* Module 1 */ /* Module 2 */int x=1; double x=1.0;void main() int p2(){ {} }(a) REF(x.1) → DEF(_____._____)(b) REF(x.2) → DEF(_____._____)1. Here is a model M:Domain: {1, 2, 3, 4, 5}P : {1, 3, 5}, Q : {2, 4, 5}, R : ∅, S : {3, 4}a : 3, b : 4Is the proposition ∀x((P x ∧ Qx) → Sx) ∨ (Rb ↔ P a) true or false in M? Explain.