Course Name: Options Trading Strategies In Python: Basic, Section No: 3, Unit No: 2, Unit type: Quiz
I can see why the mean is equal to 1 but I don't understand why stddev is equal to 2. Could you please explain that?
Cheers,
Gabriel.
Hi Gabriel,
The mean is 1 as you also agree.
For a standard normal, the graph would contain ~98.7% between -4 and 6. You can visualize the results using this tool.
Even without the tool, you can visually estimate that 2 stddev around the mean encompasses ~70% region hence the variance is 2.
Hope this helps!
Hi Gaurav,
I am still trying to understand how to be sure that the stddev is exactly 2. How do you know that is it not 1.8 or 2.2, for example? Since the question's forth answer opens the result to any other value for stddev which is different than 2.
I am supposing that you used the following approach to obtain the stddev given a chart for a X random variable:
- Look at the chart and check out its extreme values because according to the "The Empirical Rule" we can say that these extreme values represent approximately ~99.7% of that data and this is equivalue to third stddev above and bellow the mean; We could also use other regions like 95% or 68% but it is just the ~99.7 is easier to identify in the chart.
- Then, the X positive extreme value corresponds to +3 stddev and the negative one is -3 stddev.
- Divide the extreme values by 3 stddev in order to have the value of X per unit of stddev. In that case, for the positive extreme value we have 6/3=2, and then 2% of X per unit of stddev, interchangeably we can say that 1 stddev = 2% as the chosen answer and you agreed. However, there are two things that I don't agree:
- The first one, suppossing that 1 stddev=2% is the correct answer then we would have:
1 stddev around the mean is the range [-1%,+3%] ~68% of the data.
2 stddev around the mean is the range [-3%,+5%] ~95% of the data.
3 stddev around the mean is the range [-5%,+7%] ~98.7% of the data.
Thus, this contradict with what you wrote in your answer about the range for the 3th stddev: "…the graph would contain ~98.7% between -4 and 6…"
Another contradiction is when we use the negative extreme value instead of the positive one to calculate stddev: 4/3=~1.33, interchangeably 1 stddev=~1.33% which contradict to the stddev obtained previouly by using the positive value, 2%.
- The second thing is that this approach is based on a best estimate for where the ~98.7% region resids on the chart by looking at its extreme ticks and thus its accuracy depends on the precion of the ticks shown in the x-axis.
Therefore, we can, at best, have a "good" estimate for stddev but not the exact value and thus the forth answer is the correct one in my point of view.
Just for the sake of curiosity, last say that we don't care about having the exact value and just want to have the best estimate possible for stddev looking at a chart, then I think we can slightly change the second and thid step of aproach mentioned above to obtain the stddev value:
- Subtract the extreme positive value by the mean to have the X value for the third stddev then;
- Divide that result by 3 in order to have the X value per unit of stddev. In that case, for the positive extreme value we have (6-1)/3=~1.67, and then 1.67% of X per unit of stddev, interchangeably we can say that 1 stddev = 1.67% as the best estimate. Note that this also work for the extreme negative value: (-4-1)/3=-~1.67%.
Therefore, ~1.67% is the best estimate for stddev given the ticks shown on chart and thus X~N(1, 1.67).
Does it make sense?
Cheers,
Gabriel.
Hi Gabriel,
You are correct in pointing out that 3 sigma levels are -5 and 7. It should not be -4 and 6.
Also, your explanation makes sense and we shall take this up to enhance the MCQ options. The last option introduces a plethora of possibilities.
Thanks!
Thank you Gaurav.
Hi Gabriel,
The question has been updated to remove ambiguity.
Thanls!