Hello,

Please help I have no clue of where to start with this problem,

Problem: Consider one way of modeling a problem. Say you have a device, and, in any given year, there is about a 1 in 6 chance that the device will fail. A question is, "On average, how long will it be before such a device fails?" This sort of problem is what will be modeled and analyzed here.

The problem above can be modeled as follows: Roll a normal fair six-sided die. Rolling a 1 will count as "fail" anything else will count as "not-fail." The random variable we will use will be

X = # of rolls required before a 1 is rolled = "time until failure"

This is a random variable, so in each experiment (for each device) this will produce a value. For example, if we roll, then X = 5 (we count the final roll).

Part 1 (Scientific 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.

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.

Part 2 (Mathematical 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:

(Expected Value)

(Variance)

(Standard Deviation)

Repeat the second item of Part 1:Given the modeling problem we started with, interpret and in terms of how many years are expected before the device fails.