Find the shortest distance between vertices A and F using Dijistra’s algorithm for the given graph and draw the path. S = [1 1 1 2 2 2 3 3 3 4 4 5]; T = [2 3 4 3 4 5 4 5 6 5 6 6]; W = [3 5 6 3 4 7 2 6 8 2 2 5]; G = graph(S,T,W); [path,d] = shortestpath(G,1,6); P = plot(G,'Edgelabel',G.Edges.Weight); fprintf("%d\n",path); fprintf("The length %d:",d); Find the minimum spanning tree of the given graph using Kruskal’s algorithm and write its weight. S = [1 1 1 2 3 3 4 4 4 6 6 7]; T = [3 4 2 5 4 6 2 5 7 7 4 5]; W = [4 1 3 10 2 5 3 7 4 1 8 6]; G = graph(S,T,W); MST = minspantree(G,'Method','sparse'); P = plot(G,'Edgelabel',G.Edges.Weight); L =sum(MST.Edges.Weight); disp('weight of the minimum spanning tree='); disp(L); The number of particles of contamination that occur on an optical disc has a Poisson distribution, and the average number of particles is 10. Find the probability that 12 or less particles occur in the area of a disc. probability=poisscdf(x,lamda) probability=1-poisscdf(x,lamda) The marks of 1000 students in an examination follows a normal distribution with mean 70 and standard deviation 5. Find (i) no. of students whose score lies between 65 and 75 marks. (ii) no. of students whose score more than 85. probability=normcdf(x, mu,sigma) p=normcdf([65,75],70,5); p(2)-p(1); 1000*(p(2)-p(1)) probability=1-normcdf(85,70,5) 1000* 0.0013 In a certain town, the duration of shower is exponentially distributed with mean 5 minutes. What is the probability that the shower will last for (i) less than 10 minutes (ii) 10 minutes or more and (iii) between 10 and 12 minutes. mu = 5 p=expcdf(10,mu) q=1-p p2=expcdf(12,mu)-expcdf(10,mu)