Part 1 (Empirical Analysis): Roll a die, or simulate using Excel, python, or some other option, e.g., Random.org, 20 repetitions of obtaining a value for X, that is, roll until a 1 is rolled, record the result and repeat 20 times. For example, if the rolls are

, then record 4 since 4 rolls were required.

Record your rolls and counts.

Compute the mean and standard deviation of your values for X.

Given the modeling problem we started with interpret the mean and standard deviation you found in terms of how many years are expected before the device fails.

Excel might be used for this part as it makes the calculations, recording of data, etc., very simple, however, it is not required.

Part 2 (Theoretical Analysis): Compute the expected value, variance, and standard deviation of the random variable X. See the additional notes for discussion on these computations, in brief:

= the probability of rolling something other than a 1 )-times, then rolling a 1 on the i^th throw. Make a table for the first 10 values:

Use this to compute and and then use these to get a rough approximation of and

(Expected Value)

(Variance)

(Standard Deviation)