Question 1

Use the following information to answer the given subquestions.\ Consider 4 bits, where each bit can be either 0 or 1, transmitted over a noisy channel, i.e., there is a possibility of error. The probability of 1 bit getting changed is *p*, independent of all other bits. Let the random variable *X* denote the number of bits that changed. Identify the distribution of *X*. Use the following information to answer the given subquestions.\ Consider 4 bits, where each bit can be either 0 or 1, transmitted over a noisy channel, i.e., there is a possibility of error. The probability of 1 bit getting changed is *p*, independent of all other bits. Let the random variable *X* denote the number of bits that changed. Suppose the number of errors in 5 transmissions are *x*1 = 0, *x*2 = 1, *x*3 = 0, *x*4 = 2, *x*5 = 0: What is the likelihood function of p? Use the following information to answer the given subquestions.\ Consider 4 bits, where each bit can be either 0 or 1, transmitted over a noisy channel, i.e., there is a possibility of error. The probability of 1 bit getting changed is *p*, independent of all other bits. Let the random variable *X* denote the number of bits that changed. Suppose the number of errors in 5 transmissions are *x*1 = 0, *x*2 = 1, *x*3 = 0, *x*4 = 2, *x*5 = 0: Find the Maximum likelihood estimate for *p*. Enter the answer correct to two decimal places.