Exercise 5.3 An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.01 and fills are independent. 1. Determine the probability mass function of the number of fills (X) before the manufacturing line is stopped. 2. Find the probability that at least 100 fills can be completed before the manufacturing line is stopped. 3. Calculate the mean and variance of X.

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