duction: This lab focuses on using concepts in probability. We will look at Bernoulli random variables and Gaussian random variables and see how they play roles in digital communication systems. Specifically, we will simulate a Binary Symmetric Channel (BSC) and look at a binary detection problem. Provide MATLAB code. #1) Write a function in MATLAB to simulate a binary symmetric channel (BSC). The inputs should be P(X = 1) = p and P(X = 0) = 1 p. The binary symmetric channel has conditional probabilities given by P(Y = 1|X = 0) = P(Y = 0|X = 1) = and P(Y = 1|X = 1) = P(Y = 0|X = 0) = 1 . The inputs to the function should be p, , and n (the number of samples). The output should give n pairs of values of samples from (X, Y ). Also compute the analytic value of P(X = 1|Y = 1) and P(X = 1|Y = 0)