A produce dealer has a warehouse that stores a variety of fruits. He wants a machine capa of sorting the fruit according to the type. There is a conveyor belt on which the fruit is loaded. then passed through a set of sensors which measure 3 properties of the fruit: shape, texture, weight. The sensor system is somehow rather primitive: Shape sensor : -1 if the fruit is round and 1 if it is more elliptical • Texture sensor :-1 if the surface is smooth, 1 if it is rough Weight sensor :-1 if the fruit is > 500g, 1 if is < 500g

Submit solutions to the following problems in a single pdf document preferably completed using LaTeX. It is likely that you will need to use programming (Python) or a matrix calculator to solve most of the problems. You do not need to submit the code, but you should include explanations of all your conclusions. 1. Suppose a robot mouse is placed in a grid. Each room in the grid has doors that open to all other rooms. One room contains a trap so if the robot mouse enters that room, then the robot loses and the game ends. If the robot mouse makes it to the outside of the grid, then it wins and the game ends. Suppose the grid is 5x5 and the trap is in the third row, third column. When the robot mouse is placed in a room, it randomly selects a move left, right, up, or down until it is either trapped or reaches the outside. Assume that the starting point is never the room with the trap. What is the probability that the robot mouse will win the game? Does it depend on where the mouse begins?…

Using Microsoft Excel, create a spreadsheet to simulate a finite element analysis of heat transfer in a sheet of metal which is heated to soldering temperature at one corner. Assume that the temperature of any single cell is equal to the average of the temperatures of the four cells which share a side with it.   Create a 10 by 10 cell finite element model with the temperature of the top edge (all 10 cells) is held to 20 degrees C, and the temperature along the right side is also held to 20 degrees.  Make the lower left corner "hot" -- you can pick a value similar to a that of a soldering iron (look up temperatures of soldering iron tips).  You can then add values long the bottom going from high down to 20 degrees, decreasing from left to right -- choose any starting rate you like.  You can do the same for the left side, going from 20 degrees at the top and going up to the high temperature you have assigned in the lower left corner.  Once you have made sure your spread sheet model…

Three guys John, Paul and Peter are on a death row in GA. Governor decided to pardon one of them randomly chosen. He told the name of the pardoned to the gourd. Night before execution, each prisoner is in his own cell and none are  supposed to knowwho will be pardoned.  John asks the guard to give him the name from the other two who will be executed. Guard answers that Peter will be executed. John gets happier - before the guard gave him the name, his probability to survive was 1/3, and now when he knows that either him or Paul will be pardoned, his probability to survive is higher = 1/2. Is it correct? Should John be happy?(Give YOUR EXPLANATION for the probabilities for John to be pardoned))