Stats 2 Quiz 1: 11 July 2021, Set POD21QZBQPA (May 2021 term)

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 x1 = 0, x2 = 1, x3 = 0, x4 = 2, x5 = 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 x1 = 0, x2 = 1, x3 = 0, x4 = 2, x5 = 0: Find the Maximum likelihood estimate for p. Enter the answer correct to two decimal places.