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1. There is a 5-digit binary number. Random variable X is defined as the number of...

1. There is a 5-digit binary number. Random variable X is defined as the number of 0's in the binary number. (a) Draw the probability mass function (PMF) for X. (b) Draw the cumulative distribution function (CDF) for X. (c) Using the PMF, find the probability that the 5-digit binary number has at most three 0’s. (d) Using the CDF, find the probability that the 5-digit binary number has at most three 0’s. 2. Now, referring to the PMF that you found in Problem 1, you are asked to find mean and variance of the random variable X. (a) Find the mean of X. (b) Find the variance of X.

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