MAT-154
Statistics Project Final
Problem: Machines have the probability of falling 1/6 every year. I need to simulate how long
will it take to fail in average of 20 times.
Part I (Empirical Analysis):I simulated this by rolling the dice until I obtained 1 every time.
The average of the numbers I got is [4.7].This means that in average, it will take about 4.7 years
until the machine fails. The numbers I obtain in each round until I got a 1 are
[1,3,6,1,2,1,4,9,5,14,21,2,5,3,3,3,2,2,2,5]. I took the difference of these values from the mean [-
3.7, -1.7, 1.3, -3.7, -2.7, -3.7, -0.7, 4.3, 0.3, 9.3, 16.3, -2.7, 0.3, -1.7, -1.7, -1.7, -2.7, -2.7, -2.7,
0.3]. Each of these values squared are [13.69, 2.89, 1.69, 13.69, 7.29, 13.69, 0.49, 18.49, 0.09,
86.49, 265.69, 7.29, 0.09, 2.89, 2.89, 2.89, 7.29, 7.29, 7.29, 0.09]. The sum of all of the squares
are [462.2], and the divided by the sample size (20) gave me [23.11]. Taking the square root of
this give me [4.807] which is the standard deviation. In conclusion, it takes 4.7 years on average
before the machine fails, and the low standard deviation tell us that it is reliable because the
difference between numbers is small.
Part II (Theoretical Analysis-Approximations):
Now, we havethe calculations of 20 rounds. With this information we are able to calculate an
approximation of an infinite number of simulations. This includes Expected value, Variance, and
Standard deviation of the variable X(Likelihood of machine to fail). The probability (P) of the
Statistics Project Final
Problem: Machines have the probability of falling 1/6 every year. I need to simulate how long
will it take to fail in average of 20 times.
Part I (Empirical Analysis):I simulated this by rolling the dice until I obtained 1 every time.
The average of the numbers I got is [4.7].This means that in average, it will take about 4.7 years
until the machine fails. The numbers I obtain in each round until I got a 1 are
[1,3,6,1,2,1,4,9,5,14,21,2,5,3,3,3,2,2,2,5]. I took the difference of these values from the mean [-
3.7, -1.7, 1.3, -3.7, -2.7, -3.7, -0.7, 4.3, 0.3, 9.3, 16.3, -2.7, 0.3, -1.7, -1.7, -1.7, -2.7, -2.7, -2.7,
0.3]. Each of these values squared are [13.69, 2.89, 1.69, 13.69, 7.29, 13.69, 0.49, 18.49, 0.09,
86.49, 265.69, 7.29, 0.09, 2.89, 2.89, 2.89, 7.29, 7.29, 7.29, 0.09]. The sum of all of the squares
are [462.2], and the divided by the sample size (20) gave me [23.11]. Taking the square root of
this give me [4.807] which is the standard deviation. In conclusion, it takes 4.7 years on average
before the machine fails, and the low standard deviation tell us that it is reliable because the
difference between numbers is small.
Part II (Theoretical Analysis-Approximations):
Now, we havethe calculations of 20 rounds. With this information we are able to calculate an
approximation of an infinite number of simulations. This includes Expected value, Variance, and
Standard deviation of the variable X(Likelihood of machine to fail). The probability (P) of the
