Write a matlab function y = channel(x, p) that takes a vector of transmitted bits x and p as input and returns the vector of received bits y. (b) looking at the received bit y , the receiver estimates the transmitted bit in the form of xˆ. a maximum likelihood (ml) estimator uses the following decision rule to find xˆ: xˆ = ( y if p ≥ (1 − p) y¯ if p < (1 − p) where y¯ is the complementary bit to y , i. e. y¯ = 0 if y = 1, and y¯ = 1 if y = 0. show that the above decision rule is the same as the one that finds b which maximizes p[y = y|x = b] over all values of b. note both b and y can be 0 or 1. p[y = y|x = b] is called the likelihood of y given x. (c) write a matlab function xhat = mlreceiver(y, p) that takes a vector of received bits y and p as input and returns the vector of estimated bits xhat.

Kyle, a receptionist for a building supply company, recently won an award for saving his company money on their phone system. after being presented with kyle's research, the company changed the way in which it made long-distance phone calls and cut their expenses in this area by 75 percent. the new system the kyle's company most likely adopted was wired communications switching stations voip hdtv

Write a program that displays the following menu: geometry calculator 1. calculate the area of a circle 2. calculate the area of a rectangle 3. calculate the area of a triangle 4. quit enter your choice (1-4): if the user enters 1, the program should ask for the radius of the circle and then display its area. use the following formula: area = ď€(the square of r) use 3.14159 for ď€ and the radius of the circle for r. if the user enters 2, the program should ask for the length and width of the rectangle and then display the rectangle’s area. use the following formula: area = length * width if the user enters 3, the program should ask for the length of the triangle’s base and its height, and then display its area. use the following formula: area = base * height * .5 if the user enters 4, the program should end. input validation: display an error message if the user enters a number outside the range of 1 through 4 when selecting an item from the menu. do not accept negative values for the circle’s radius, the rectangle’s length or width, or the triangle’s base or height. note: if the user enters an improper menu choice (1-4), the program prints "the valid choices are 1 through 4. run the program again and select one of those." if the user enters a negative radius, the program prints "the radius can not be less than zero." if the user enters a negative value for height or base, the program prints "only enter positive values for base and height."

In simple terms, how would you define a protocol?